{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"写在前面：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"大家好，我是强哥，一个热爱分享的技术狂。目前已有 12 年大数据与AI相关项目经验， 10 年推荐系统研究及实践经验。平时喜欢读书、暴走和写作。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"业余时间专注于输出大数据、AI等相关文章，目前已经输出了40万字的推荐系统系列精品文章，今年 6 月底会出版「构建企业级推荐系统：算法、工程实现与案例分析」一书。如果这些文章能够帮助你快速入门，实现职场升职加薪，我将不胜欢喜。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"想要获得更多免费学习资料或内推信息，一定要看到文章最后喔。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"内推信息","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你正在看相关的招聘信息，请加我微信：liuq4360，我这里有很多内推资源等着你，欢迎投递简历。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"免费学习资料","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想获得更多免费的学习资料，请关注同名公众号【数据与智能】，输入“资料”即可！","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"学习交流群","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想找到组织，和大家一起学习成长，交流经验，也可以加入我们的学习成长群。群里有老司机带你飞，另有小哥哥、小姐姐等你来勾搭！加小姐姐微信：epsila，她会带你入群。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们在第十六章协同过滤推荐算法中介绍了经典的item-based协同过滤推荐算法。在本章中我们会继续介绍三种思路非常简单朴素的协同过滤算法，这几个算法的原理简单，容易理解，也易于工程实现，非常适合我们快速搭建推荐算法原型，并快速上线到真实业务场景中，作为其他更复杂算法的baseline，提供效果对比参考。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"具体来说，我们在本章中会介绍利用关联规则、朴素贝叶斯(naive bayes)、聚类三类机器学习算法来做协同过滤推荐的方法。并且还会介绍3个核心思想基于这三类机器学习算法的工业级推荐系统，这3个推荐系统被YouTube和Google分别用于视频和新闻推荐中(其中会介绍Google News的两个推荐算法)，这些算法在YouTube和Google News早期产品中得到采用，并且在当时情况下效果是非常不错的，值得我们深入了解和学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.1 基于关联规则的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"关联规则是数据挖掘领域非常经典的算法，该算法来源于一个真实的案例：“啤酒与尿布”的故事。该故事发生在20世纪90年代的美国沃尔玛超市中，沃尔玛的超市管理人员分析销售数据时发现了一个令人难以置信的现象：在某些特定的情况下，“啤酒”与“尿布”两件看上去毫无关系的商品会经常出现在同一个购物篮(用户一次购物所买的所有商品形象地称为一个购物篮)中，这种独特的销售现象引起了管理人员的注意，经过后续调查发现，这种现象出现在年轻的父亲身上。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在美国有婴儿的家庭中，一般是母亲在家中照看婴儿，年轻的父亲前去超市购买尿布。父亲在购买尿布的同时，往往会顺便为自己购买啤酒，这样就会出现啤酒与尿布这两件看上去毫不相干的商品经常会出现在同一个购物篮的现象。沃尔玛发现了这一独特的现象，开始在卖场尝试将啤酒与尿布摆放在相同的区域，让年轻的父亲可以方便地同时找到这两件商品，并很快地完成购物。这样做沃尔玛超市就让这些客户一次购买了两件商品、而不是一件，从而获得了很好的商品销售收入，这就是“啤酒与尿布”故事的由来。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我们给出关联规则的定义，假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/10/10f575e56de5600a4ae2d36db284fb2d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是所有标的物的集合(对于沃尔玛超市来说，就是所有的商品集合)。关联规则一般表示为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 的形式，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4c/4cb50d0ce11a7a10e9e835d0bf016326.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0b5e39df54538b7d3ff7ce20e1a254f8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的子集，并且","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/22/22079c0bfee2a2a89dd8dc1dd28fb877.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示如果","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在用户的购物篮中，那么用户有很大概率同时购买了","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。通过定义关联规则的度量指标，一些常用的关联规则算法(如Apriori)能够自动地发现所有关联规则。关联规则的度量指标主要有","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"支持度(support)","attrs":{}},{"type":"text","text":"和","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"置信度(confidence)","attrs":{}},{"type":"text","text":"两个，支持度是指所有的购物篮中包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/33/33db192393da378bb603f67324899e66.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的购物篮的比例(即","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4c/4cb50d0ce11a7a10e9e835d0bf016326.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同时出现在一次交易中的概率)，而置信度是指包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的购物篮中同时也包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例(即在","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"给定的情况下，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"出现的条件概率)。它们的定义如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78de2f5125aec1dbe8288636c7a6e8e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5e/5e31009ad08de2759fefb954d787c148.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"支持度越大，包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/33/33db192393da378bb603f67324899e66.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的交易样本越多，说明关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有更多的样本来支撑，“证据”更加充分。置信度越大，我们更有把握从包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的交易中推断出该交易也包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。关联规则挖掘中，我们需要挖掘出支持度和置信度大于某个阈值的关联规则，这样的关联规则才更可信，更有说服力，泛化能力也更强。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了关联规则的定义，下面我们来讲解怎么将关联规则用于个性化推荐中。对于推荐系统来说，一个购物篮即是用户操作过的所有标的物的集合。关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示的意思是：如果用户操作过","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的所有标的物，那么用户很可能喜欢","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的标的物。有了这些说明，那么利用关联规则为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"生成推荐的算法流程如下(假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有操作过的标的物集合为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f5/f5fde0280c0e5db9eadae1c57b8a4807.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 挖掘出所有满足一定支持度和置信度(支持度和置信度大于某个常数)的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"2. 从1中所有的关联规则中筛选出所有满足","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9d/9d52f7f4f737c9f9057b3d90c47d6fd7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"3. 为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"生成推荐候选集，具体计算如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ff/ffa3896025e7ce0a4a1b3dd814e1ade7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"即将所有满足2的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"合并，并剔除掉用户已经操作过的标的物，这些标的物就是待推荐给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的。对于3中的候选推荐集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，可以按照该标的物所在关联规则的置信度的大小降序排列，对于多个关联规则生成同样的候选推荐标的物的，可以用置信度最大的那个关联规则的置信度。除了可以采用置信度外，也可以用支持度和置信度的乘积作为排序依据。对于4中排序好的标的物，可以取topN作为推荐给用户的推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于关联规则的推荐算法思路非常简单朴素，算法也易于实现，Spark Mllib中有关联规则的两种分布式实现","attrs":{}},{"type":"link","attrs":{"href":"http://spark.apache.org/docs/latest/ml-frequent-pattern-mining.html#fp-growth","title":null,"type":null},"content":[{"type":"text","marks":[{"type":"underline","attrs":{}}],"text":"FP-Growth","attrs":{}}]},{"type":"text","text":"和","attrs":{}},{"type":"link","attrs":{"href":"http://spark.apache.org/docs/latest/ml-frequent-pattern-mining.html#prefixspan","title":null,"type":null},"content":[{"type":"text","marks":[{"type":"underline","attrs":{}}],"text":"PrefixSpan","attrs":{}}]},{"type":"text","text":"，大家可以直接拿来使用(关于这两个关联规则挖掘算法的实现细节，读者可以阅读参考文献10、11、12)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"关于关联规则算法的介绍及怎么利用关联规则进行个性化推荐，读者还可以阅读参考文献4、5、6、7、8、9。利用关联规则做推荐，是从用户的过往行为中挖掘用户的行为模式，并用于推荐，只用到了用户的行为数据，因此利用关联规则做推荐也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.2 基于naive bayes的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"利用概率方法来构建算法模型为用户做推荐，可以将预测评分问题看成一个分类问题，将可能的评分离散化为有限个离散值(比如1、2、3、4、5一共5个可行的分值)，那么预测用户对某个标的物的评分，就转化为用户在该标的物上的分类了(比如分为1、2、3、4、5个类别，这里不考虑不同类之间的有序关系)。在本节我们就利用最简单的贝叶斯分类器来进行个性化推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假设一共有k个不同的预测评分，我们记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d029b3077eaeaa602828adf1bdcd4fe4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，所有用户对标的物的评分构成用户行为矩阵","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/28/28c0efcd8cb2b85b45a681ad5deddcb1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，该矩阵的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0bca50881ea2309ffeb904896030f691.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"-元素记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/556ff0654442219f13cff874fc33f776.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即是用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/27/2747df64c9962eabc30e110288bc1af5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分，取值为评分集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的某个元素。下面我们来讲解怎么利用贝叶斯公式来为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"做推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假设用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有过评分的所有标的物记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e4/e4ba2d2682f317d2142fe6060f88eaac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。现在我们需要预测用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对未评分的标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/77/77e88c3b80690657e3f48a5e21d1575c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")。我们可以将这个过程理解为在用户已经有评分记录","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的条件下，用户对新标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中某个值的条件概率：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"条件概率","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/06eb881946e17f1c4eaa4285dd13215c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，表示的是在事件","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a7860bd927513eb3e3e59b48de9ee2d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"发生的情况下事件","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f5/f5fde0280c0e5db9eadae1c57b8a4807.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"发生的概率，由著名的贝叶斯定理，条件概率可以通过如下公式来计算：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3898ed74b47c0813d9bb195f6cf62990.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因此，回到我们的推荐问题，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce13daa025667649f6edda548ccd06d1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/62/622a18b91784d956935c3742052c3fde.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们需要确定具体的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"值，让上式左边的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值最大，这个最大的值","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8f/8f2ebdc872d90ebd7810f31ebdd451a5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就可以作为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对未评分的标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"=","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8f/8f2ebdc872d90ebd7810f31ebdd451a5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")。我们注意到上式中右边的分母的值与具体的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"无关，因此右边分子的值的大小才最终决定公式左边的值的相对大小，基于该观察，我们可以将上式记为：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3efdf0f90bea89611d96e597acfa4559.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"现在的问题就是怎么估计上式右边项的值，实际上基于用户评分矩阵，这些项的值是比较容易估计出来的，下面我们就来估计这些值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其实是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1de4ba7abadcf5360e6fc1db76f482c3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的先验概率，我们可以用对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户的比例来估计该值，即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/61098f16b42a2980e5aa589873d89ed5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里分母是所有对标的物","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有过评分的用户，而分子是对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"要估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们需要做一个朴素的假设，即条件无关性假设：用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是独立无关的，也就是不同的评分之间是没有关联的，互不影响(该假设就是该算法叫做naive bayes的由来)。实际上，同一用户对不同标的物评分可能是有一定关联的，在这里做这个假设是为了计算方便，在实际使用naive bayes做推荐时效果还是很不错的，泛化能力也可以。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了条件无关性假设，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就可以用如下公式来估计了：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2b/2b23cb81a4f7e39ab34e3290dff9caf8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/69/69c43e39d282f5bacccdd2c71f1273f5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可用所有对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户中对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/62/625fe11fcdfe277ff5ee1e0b82e51ae3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ec/ecc054779d194a4f806b7a33a42ac988.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例来估计。即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ca/ca01a319b0ef24ec70f044226b65f439.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面的两个估计，那么我们利用naive bayes计算用户对标的物的评分概率问题最终可以表示为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ec/ec24965db859ecf9a5f18c5f1c7f783e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"size","attrs":{"size":10}}],"text":"公式1：用户对标的物评分的概率估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上式，一般来说，我们可以采用两种方法来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8d/8dd0a304c30df6acb81f0e3e787506e2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 类似极大似然的思路估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法就是用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2e/2ed42750f5567ea3d4a7cabe24ded447.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，使得","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取值最大的p对应的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"作为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1de4ba7abadcf5360e6fc1db76f482c3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计值，即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/31/31a5aa93a34cf906d94faac1349d0f90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法仅仅将用户对标的物的评分看为类别变量而忽略具体评分的数值，而下面的方法则利用了评分的具体数值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"采用加权平均来估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef3aefc8da69c0f667da6d02060ffd86.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可以取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ca/cabe5d856a72918812ec4217c941a41f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的任一值，基于上面的公式1，取每一个值都有一个概率估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么最自然的方式是可以用这个概率作为权重，利用加权平均来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c8/c8330daacddda7697f407fa297ba1b34.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，具体的估计公式如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4a/4af511d78ae35989431d639c6a41bc1a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了用户对标的物评分的估计，那么推荐就是顺其自然的事情了。具体来说，我们可以计算出用户对所有未评分标的物的估计值，再按照估计值的大小降序取topK作为给用户的推荐。这里说明一下，对于采用极大似然思路的估计(即上面的第一种估计方法)，因为该方法是将评分看成类别变量，那么肯定有很多标的物的估计值是一样的，这时如果我们需要再区别这些评分一样的标的物的话，可以采用估计该值时的概率大小再进行二次排序。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"采用贝叶斯方法来做推荐会存在一些问题，具体来说，我们在估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"和估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，由于样本数据稀疏，导致无法进行估计或者估计值不够鲁棒性的问题。比如在估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，我们用公式","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/61098f16b42a2980e5aa589873d89ed5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来估计，从该式可以看到，如果无用户或者很少用户对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有评分(这种情况是存在的，如","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是新加入的标的物或者是冷门标的物)，这时可能会出现用 ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dd/dd878cc6534016e300a2742223eef033.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 来估计的情况，即使不是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dd/dd878cc6534016e300a2742223eef033.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，当分子分母都很小时，估计值波动会很大，不够鲁棒，对估计结果影响很大。一般我们可以采用拉普拉斯平滑(Laplacian smoothing)的方法来处理，得到更加稳定的估计值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"针对上面这个例子，我们来说下怎么利用拉普拉斯平滑来处理：假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1da0a3e6e3bfe1044f786ab028e19ced.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分分别为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e8/e8c3e3f48b063dc75a8f817d23f49ad1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户数，那么上面的估计就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/36/36f57954ec3eac5a20523f56ce7646d3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"增加拉普拉斯平滑后的估计公式就是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b17af01eba0bb80f0e645ae8e969b7dc.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从这个公式可以看出，当没有用户对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评过分时，就用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3ed596c8138fe9b87243fdbd1e4d74b7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来估计，这是在没有已知信息的情况下比较合理的估计。上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/075b484a80fde9e9a75b3cdf599af16d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是光滑化因子，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/075b484a80fde9e9a75b3cdf599af16d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"值越大，估计越光滑(鲁棒性越好)，这时公式对数据就不够敏感。对于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计，也可以采用一样的方法，这里不再赘述。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到此为止，我们讲完了怎么利用naive bayes来为用户做推荐的方法，该方法也是只利用了用户的操作行为矩阵，所以也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"naive bayes方法是一个非常简单直观的方法，工程实现也非常容易，也易于并行化。它对噪音有一定的“免疫力”，不太会受到个别评分不准的影响，并且也不易于过拟合(个人觉得前面介绍的条件无关性假设是泛化能力强的主要原因)，一般情况下预测效果还不错，并且当用户行为不多时，也可以使用(需要利用拉普拉斯平滑来处理)，而不像矩阵分解等算法，需要大量的用户行为才能进行推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"读者可以从从参考文献13、14、15、16中了解更多关于怎么利用贝叶斯及其他概率方法来做推荐的方案。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3 基于聚类的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于聚类来做推荐有两种可行的方案，一种是将用户聚类，另外一种是将标的物聚类。下面来简单描述一下怎么基于这两种聚类来做推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3.1 基于用户聚类的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果我们将所有用户聚类了，就可以将该用户所在类别的其他用户操作过的标的物(但是该用户没有操作行为)推荐给该用户。具体计算公式如下，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f8/f8a96beda26f47dfeeeeda787343463e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是给用户u的推荐，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户所在的聚类，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ac/ac34fa6802ecef1ad881eb76e49141fc.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4b/4b49d6e8dfe81bc88d07f5c21ee003e7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"分别是用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a7/a782d6c46919465c474437c36468ccbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的操作历史集合。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a4/a4ea8cc28805ac4e769fdf17a77d0402.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么怎么对用户聚类呢？可行的方案主要有如下几类：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(1) 基于用户的人口统计学特征对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用户的年龄、性别、地域、家庭组成、学历、收入等信息都可以作为一个特征，类别特征可以采用one-hot编码，所有特征最终都可以转化为数值的，最终获得用户特征的向量表示，通过Kmeans聚类算法来对用户聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 基于用户行为对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"比如采用矩阵分解就可以获得用户的嵌入表示，用户操作行为矩阵的行向量也是用户的一种向量表示，再利用Kmeans对用户进行聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(3) 基于社交关系对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果是社交产品，用户之间的社交链条可以构成一个用户关系图，该社交图中所有的联通区域就形成了用户的一种聚类。这种推荐其实就是将你的好友喜欢的标的物推荐给你。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3.2 基于标的物聚类的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果有了标的物的聚类，推荐就好办了。从用户历史行为中的标的物所在的类别挑选用户没有操作行为的标的物推荐给该用户，这种推荐方式是非常直观自然的。具体计算公式如下，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f8/f8a96beda26f47dfeeeeda787343463e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的推荐，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7b/7b407c68ca521579f54061f76b81cf0e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户的历史操作行为集合，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a0e7d428c6c5baa7549f6f597f2426f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所在的聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8e/8ea259bd8eb4f2246a4e99ecf0165195.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同时，有了标的物聚类，我们还可以做标的物关联标的物的关联推荐，具体做法是将标的物A所在类别中的其他标的物作为关联推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么怎么对标的物聚类呢？可行的方法有利用标的物的metadata信息，采用TF-IDF、LDA、Word2vec等方式获得标的物的向量表示，再利用Kmeans聚类。具体的实现细节这里不介绍，感兴趣的读者可以自行搜索相关材料做深入学习，作者在第五章《基于内容的推荐算法》中也做了比较详细的介绍。另外，也可以基于用户的历史操作行为，获得标的物的嵌入表示(矩阵分解、item2vec等算法)，用户行为矩阵的列向量也是标的物的一种向量表示。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"参考文献17、18、19、20有更多关于怎么用聚类来做推荐的算法，感兴趣的读者可以参考学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到此为止，我们讲完了基于关联规则、naive bayes、聚类做个性化推荐的方法。下面我们就基于这几个方法的思想来介绍三个工业级的推荐引擎，供大家学习参考，同时也希望借助这几个工业级推荐系统的介绍让大家加深对这三个方法的思路的理解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4 YouTube基于关联规则思路的视频推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"YouTube基于关联规则思路的视频推荐算法(见参考文献1)建立在一个基本假设基础之上：如果用户喜欢种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么用户喜欢与种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"相似的候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率一定很大，候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越相似，那么用户喜欢候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率也越大。那么剩下就是怎么解决这两个问题了：一是怎么计算两个视频的相似度，二是怎么选择种子视频，下面我们来分别介绍。同时，我们也会介绍最终怎么给用户生成个性化推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.1 计算两个视频的相似度(关联度)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该算法是利用关联规则的思路，在一定时间内(比如24小时内)统计两两被用户同时播放过的视频对","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/bea12e797c1b852eb00b88566fcf8da1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，将播放次数计为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/aa/aa34d8d2b59d55b38278e7e65e5474d0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度可以表示如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e7/e7042221e3714874fc5823af015ea028.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f6/f6b74fcb97d71ceab7c15fcb8ef198e8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是一个归一化常数，会综合考虑种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的“全局流行度”，如果我们分别记","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在上面的一段时间内总的播放次数。那么我们可以定义","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/6197d9d468abc64e08c41b3b1a31f7b5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该归一化函数是非常直观简单的，用其他归一化函数也是可以的。如果用该归一化函数的话，对所有候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来说，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是一样的，所以可以忽略，其实我们是用候选视频的“全局流行度”","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来归一化。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在分母中，这说明","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越大的视频，与种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度会更小，该归一化方法更加偏向于偏冷门的候选视频。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面只是一个非常简单的描述和计算公式，我们也可以将视频的metadata、观看时间等信息整合进来计算相似度。另外，还需要处理脏的播放行为数据。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.2 基於单个种子视频生成候选视频集","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于相似度计算公式","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c11ca2ccbf9c889ba0fe64dd0c5fe4d8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们可以选择出种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的最相似的topN候选集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a2/a22a20d87fbb62ee9267b46cb32b9dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，一般我们会确定一个最小的阈值，需要相似度大于该阈值才会选出来，这也是为了避免选择很多只有很少播放量的视频(这时种子视频和候选视频被同时播放的次数也很小)导致推荐结果太差。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于上述从种子视频选择候选视频的规则，我们可以构建一个有向图。将所有视频集合构成一个有向图，对于任何一个视频对","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/bea12e797c1b852eb00b88566fcf8da1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，如果","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a9a82d14a60740e96d8daffbf93430be.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似视频列表集中)，那么存在一条从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的边，边的权重为这两个视频的相似度","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c11ca2ccbf9c889ba0fe64dd0c5fe4d8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"利用该方式为种子视频生成的视频候选集，可以作为视频的关联推荐，为种子视频推荐相关的视频。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.3 基于用户行为为用户生成推荐候选集","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面讲到了单个视频怎么生成候选集，那么对於单个用户也是很容易采用上面的方式生成推荐候选集的。我们可以将用户播放过的视频或者明确表示过喜欢的视频作为初始种子视频集。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于初始种子集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们可以采用如下方式来生成候选集：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于上面视频的有向图解释，我们可以沿着集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的有向边向外拓展，对于任意的种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2f/2fd82b8b38d3a5bffa54ce6929085c8d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，我们考虑它的相关视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a2/a22a20d87fbb62ee9267b46cb32b9dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。我们将所有通过这种方式拓展出的视频集记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49fab68263c5ad4a9db908b14cb62abb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"一般情况下，我们计算出","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就足够获得比较多的、效果还可以的、有一定多样性的推荐候选集了。但实际上，通过这种方式生成的推荐候选集种类比较狭窄，跟用户的兴趣太相似。这种方式虽然生成了用户可能感兴趣的视频，但是可能用户没有太多惊喜，会让用户沉浸在比较小的视频范围内，就像进入了一个漩涡中，无法发现更大更精彩的世界。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为了拓展用户的候选推荐集的空间，解决上述越推越窄的问题，我们可以沿着种子视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所在的视频有向图进行n次向外拓展(用图论的术语，就是n次传递闭包)，我们记","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/01/018e89b840196237917dd30cee1df40a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为通过种子集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的某个种子视频通过不超过n次路由可达的所有视频组成的集合，那么我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c2/c2b222ec07f1ec1777b7c95e978fe48e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"注意，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/26/2610cbb553a884e23fca6e4ab0b60808.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，上面的公式也跟前面提到的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的公式是兼容的。那么我们最终生成的推荐候选集就是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2a/2a27fba5c3fc7920462fc728ac918662.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"一般N很小(拓展很少的几步)时就可以获得非常多具备多样性的推荐结果，即使对种子集很小的用户也是如此。通过上述路径拓展，我们可以为每个候选的推荐视频关联一个种子视频(通过上述拓展，从某个种子视频到候选视频的路径就将候选视频关联到了种子视频)，该种子视频既可用于后面的推荐结果排序，还可以作为推荐解释(例如如果候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"获得的，我们可以用“因为你喜欢/看过","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"”来作为推荐解释语，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过多步相似链接在一起的，它们多少是有一些相似性的，用户从这两个视频中是可以直接感知到这种相似的，所以该推荐理由是有一定说服力的)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.4 推荐结果排序","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过上面7.4.3中的介绍，我们可以为用户生成推荐候选集了，那么这些候选集中的视频怎么推荐给用户呢？也即我们怎么对这些候选视频排序呢？我们需要将用户更愿意点击的排在前面。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以从视频质量、用户对视频的偏好度、多样性等几个维度来考虑。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"视频质量是指视频本身的吸引力，比如视频的海报清晰度、视频播放次数、视频被点赞的次数、视频被转载的次数、视频被收藏的次数等。这些不同维度的视频质量，我们可以通过打分获得一个固定的质量得分，具体打分方式可以多种多样，这里不再细说。我们这里记视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/111d380bcea903d6659fe965616f0437.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的质量为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/707b45b3dc6a33ba782451de2d519dab.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过前面的介绍我们知道每个候选视频是通过某个种子沿着有向图通过若干步的拓展获得的。如下图，假设候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"经过k步获得，下图中箭头上方的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9b/9bb641d69bf9e8227258e729b2a1da04.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是相邻两个视频的相似度。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/077b1cf3171fba200dfcfb395aa0364a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么用户对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的偏好度可以用如下公式来计算","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b69f24666a4b38ced3309c25546cbf94.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其中，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7c/7c188113708f2be571f40f1437fa899b.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的偏好度及它自身的受欢迎程度，我们可以通过用户播放","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的时长或者","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"总播放量等数值来度量。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有多条路径，可以选择最短的路径，这是因为我们是一步一步拓展获取候选集的，当某个视频被某一步拓展到了，后面再拓展到它时，前面已经计算了，所以在这一步就忽略掉。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面介绍的候选视频得分及用户对视频的偏好度，我们可以用下面公式来计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最终的评分：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0bc0ba7fe13c692e042dd73de61f8bc4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过将所有候选视频按照上述公式降序排列就可以得到候选视频的排序了。利用上面公式，距离用户种子视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越远，通过公式","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3e93f2d033b09d3e1e66b8f6eec41281.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 的相似性连乘得到的值也越小，那么就有可能排在后面了。那么我们怎样解决这个问题获得多样性呢？一般我们可以通过限制由同一种子视频生成的候选视频的数量来获得多样性(因为同一种子视频生成的视频多少是有一些相似度的)，或者限制由同一渠道产生视频数量(比如由同一个用户上传的视频)。通过在上述排好序的推荐列表中，剔除掉部分由同一种子视频生成的视频或者同一渠道产生的视频，就可以获得最终的推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面介绍的就是YouTube基于视频被用户共同观看的次数获得视频之间的相似度，进而通过视频相似度传递获得最终推荐的方法。该方法本质上就是关联规则的思路，只用到了用户的播放行为信息，因此也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5 Google News基于贝叶斯框架的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前面7.2节简单讲了怎么利用naive bayes算法来为用户生成个性化推荐的一般思路，在这一节我们讲解Google News利用贝叶斯框架来做推荐的具体方法。Google的这篇文章(参考文献2)采用另外的思路，基于用户过去看新闻的历史行为利用贝叶斯框架来预测用户当前对新闻的兴趣，再结合协同过滤来做推荐。下面我们来讲解该篇文章的核心思想。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.1 基于用户过去的行为来分析用户的兴趣点","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先将所有新闻按照事先确定好的类别分成若干类(主题)：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bc778a25c30535de42dc87abe5ebe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，如“世界”、“体育”、“娱乐”等类别。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先计算某个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在某段时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(比如按照一个月一个周期等)内的点击行为在上述类别上的分布，记为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d0af070680a56f3bd97ef511923f92b5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式1：用户u在时间周期t内的行为在新闻主题上的分布","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/01/0164404b5bc457d4ef358b6d1e96a89b.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"代表用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内点击主题类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的次数。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d4/d4a7f7490f4f0106d5152202f097afaa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是该用户在这段时间周期内点击新闻的总数量。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内在各个新闻主题类别上的时间花费分布，反映了用户的兴趣分布。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"新闻是有地域差异性的，同样地，类似单个用户的兴趣偏好分布，我们可以统计某个国家或者某个地区的所有用户点击行为的整体在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内在上述新闻主题上的分布。我们将该分布记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。计算方法和上面单个用户一样，将该国家或地区所有用户当成一个整体来计算。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该文章通过大量的数据分析，最终得到如下4个结论，后面的贝叶斯框架也是基于这几个结论来展开的。细节的分析读者可以阅读参考文献2。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(1) 用户的兴趣确实随着时间变化；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(2) 公众对新闻的点击分布反映了兴趣的发展趋势，并受到重大事件(如世界杯等)的影响；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(3) 不同国家/地区对新闻的偏好是不一样的，存在不同的发展趋势；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(4) 从某种程度上说，单个用户的兴趣变化趋势是受到该用户所在国家/地区的新闻趋势变化影响的；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面的基本概念和初步数据分析得到的结论作为基础，下面我们来说明怎么用贝叶斯框架来为用户的兴趣建模。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.2 利用贝叶斯框架来建模用户的兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以将用户的兴趣分为两种：一种是用户的真实兴趣，一种是会受到国家/地区大的兴趣趋势影响的临时兴趣。用户的真实兴趣是由用户的性别、年龄、受教育程度、专业等决定的，它是相对稳定的，不太会随着时间而急剧变化。另一方面，当用户觉得要读什么新闻时，是会受到用户所在区域新闻趋势的影响的，这种影响是短期的，是随着时间变化的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于用户点击行为模式和用户所在地群体的行为模式，可以通过贝叶斯框架很好地预测用户当前对新闻的兴趣，具体可以通过如下三个步骤来获得用户的当前兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(1) 预测用户在某个时间周期内的真正兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于特定时间周期","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内的某个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户在所有新闻主题上的点击分布，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户所在地域整体用户的兴趣分布，代表的是兴趣趋势。我们期望学习用户的从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"呈现出的而不会受到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"干扰的真实兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示用户在新闻主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上的真实兴趣，它是一个条件概率，表示在新闻主题为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的条件下，用户进行点击的概率。利用贝叶斯公式，我们可以采用下式来计算","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/41/4121995498205c1ab1b3b12ff91f7316.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式2：用户点击属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的文章的概率","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/0740d669ce82a10b7d284aa48a739a8d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户点击的所有新闻中该新闻属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率，它可以从用户的点击分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中估算出(参见上面的公式1，可以用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的第i个分量来估算)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d935e80c2453c95b6fb816aeec86dbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是新闻属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的先验概率，也就是在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内所有发布的新闻属于类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例，它与用户所在地域的新闻变化趋势相关，如有有更多的有关主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的新闻事件发生，那么关于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的新闻就会越多。我们可以用整体分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的第i个分量来近似估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d935e80c2453c95b6fb816aeec86dbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5c/5c8140b53c9fc6345448b8880c400615.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户点击任何一个类别的文章的先验概率，与具体的文章主题无关。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从上面公式2知道，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示用户对主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的感兴趣程度，不同于该地区其他用户的兴趣。如果用户读了很多体育类的新闻，而很多其他用户也读了体育类新闻，这可能是有一些体育相关热点事件引起的。相反，如果该用户阅读了大量体育新闻而该地区其他用户很少读体育新闻，这就代表的是用户真的对体育感兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 结合用户在不同时间周期的兴趣，获得用户精确的与时间无关的真实兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面(1)中计算了用户在一个时间周期","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内的兴趣偏好，我们可以将用户在过去统计周期内所有时间周期的兴趣归并起来获得用户综合的对新闻类别的真实兴趣偏好，具体参见下面公式的计算逻辑。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4e/4e899406ddcadbe9fd235c04722cc997.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4e/4e899406ddcadbe9fd235c04722cc997.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9e/9eb5f16df9d10f8e4d32386603a6d40a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内总的新闻播放量。我们可以假设用户在所有时间周期内点击一篇新闻的先验概率是固定不变的，也即假设上式中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c4/c4d882f2951d4d3a496f6cee5f2e7aa7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"无关，我们记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e1/e13042d36dcba643f2b7aa9088284e70.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。那么上式可以改写为下面的","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/65/65c2312ac858017017b80f30f48e0318.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式3：用户在过去统计周期内所有时间段的综合兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的公式3就是用户的真实兴趣，该兴趣其实是用户在多个时间周期内的兴趣的某种加权平均。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(3) 结合用户真实兴趣和当前的新闻趋势，预测用户当前的兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如前面所说，用户的兴趣可以分解为两部分，一部分是用户长期的的真实兴趣，另外一部分是受到当前趋势影响的短期兴趣。(1)、(2)基于用户过去的点击播放行为计算出了用户的长期的真实兴趣。为了度量用户当前对新闻的短期兴趣，我们用用户所在地域的所有用户在一个较短时间段(比如过去一个小时)的整体点击分布来刻画(用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/29/299165c09284ff58330d00b0bf4b52c4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示)，由于所在地域有大量用户，在这段较短时间内也有足够多的数据来准确计算出哪些新闻主题是热门的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们的最终目标是预测用户在将来一段时间的点击分布，同样地，我们可以用贝叶斯公式得到下面的计算公式：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/09/09de797bfbe6b86428104f17d948b95c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们用用户的真实兴趣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e0/e0426b9e90d0468cedbdc10677ae64c2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(公式3)来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dc/dc087d2a66753eef9635cacebe1cadb3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，并且假设用户点击任何一篇新闻的概率为常数，不受时间影响(即假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/10/1055dd12983b5c06d0e8bdf6494d4b25.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"=","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e7/e75c70ea57b3aaee155253f91d8819fb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，那么上式就可以表示为(将公式3代入进来)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d4/d418d08d9bc8ae7abde252fc36ff54f4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以在上式中加上一个虚拟点击项，它跟当前新闻趋势的概率分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c134c11f0e434d95c65752cd9fb109f5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同分布，那么用户在未来短时间内对新闻的兴趣偏好概率最终变为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7a/7a908144ca516e687940fd02d131a03f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式4：用户当前对新闻主题的兴趣偏好概率","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就是虚拟点击数(在参考文献2中取值为10)，它可以看成是一个光滑化的因子，当某个用户只有非常少的点击历史时，这时是用户当前的新闻趋势(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ee/ee3477f4ce71893a8d1f766b3d993219.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")来预估该用户的点击概率，这在没有太多该用户历史数据的情况下是一个合理的估计。当","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7c/7c7a7b79351ff3c51248d98ccc9ae79c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"远远大于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，上式就可以忽略","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，还原为用户真实的点击分布预估。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上述预估用户将来短时间内的兴趣分布的方法的一个重要优点是，我们可以增量地计算用户的点击分布。我们可以将过去每个时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对应的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6feb409afa05e093607793382d8241c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"和","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6f/6fbb66310067cb02f2beed3e6a4b4cd7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值事先存起来，当更新用户的兴趣偏好概率时，只需要将最近一个时间周期的值计算出，利用上面的公司4及预先存下来的过去时间段的值就可以得到用户最新的兴趣偏好分布。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.3 为用户做个性化推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为了对推荐候选集进行排序获得最终的推荐结果，该推荐算法计算出两个统计量：一个是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d1/d1fff0932d64af440746e1f69233870c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，称之为信息过滤得分，另外一个是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/8146c5fa738688e3cc99a6490bd283d0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即协同过滤得分(利用协同过滤算法预测的用户对新闻的得分，可以利用参考文献3中的方法得到)。其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的计算过程是这样的，先获得该文章的类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，再基于上面的公式4得到用户对类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的的偏好概率，该值作为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1a/1acd5c87caa2fb38fbf2a3f0226a3729.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值。我们将这两个得分相乘，最终利用如下的公式来计算用户对某个新闻的兴趣得分。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b5/b5afc00e35e230005f2f83d811cc3ef3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最终基于上述公式计算出该用户对所有新闻的得分，取得分最高的topN作为最终的推荐结果。该方法通过在Google news上验证，比单独采用协同过滤有更好的预测效果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法利用用户过去及用户所在地区的点击行为来预测用户当前对新闻的偏好概率，再与协同过滤结合进行最终的推荐。预测用户兴趣偏好概率的过程只用到了用户及用户所在地域全体用户对新闻的点击数据，因此也是一种协同过滤方法。细节的实现方案，读者可以阅读参考文献2进行进一步了解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6 Google News基于用户聚类的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"参考文献3中利用了3种模型来预估一个用户对一个新闻的评分，最终通过加权平均获得用户对新闻的最终评分，其中第三种方法covisitation的思想我们在第6章《协同过滤推荐算法》第6节“近实时协同过滤算法的工程实现“有详细讲解，本质上是一种关联规则的思路，我们这里不再介绍。另外两种算法分别是基于MinHash和PLSI聚类的方法，在这里我们只介绍MinHash算法，PLSI算法读者可以自行阅读参考文献3来了解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6.1 基于MinHash聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，他的点击历史记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。那么两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/83/83420fe338ed63e05e679d085981a8e0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度可以用Jaccard系数来表示：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f1/f1d9daa149033398ec80d1f65ecc1b87.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了两个用户之间的相似度，我们可以非常形式化地将相似用户点击过的新闻通过上面的相似度加权推荐给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。但是用户数和新闻数都是天文数字，无法在极短时间内为大量用户完成计算。这时，我们可以采用LSH(","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"L","attrs":{}},{"type":"text","text":"ocality ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"S","attrs":{}},{"type":"text","text":"ensitive ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"H","attrs":{}},{"type":"text","text":"ashing)的思路来计算，大大减少计算复杂度。LSH的核心思想是，对于一组数据(对于我们这个场景来说，这一组数据就是用户的历史点击记录","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，我们可以用一组哈希函数来获得哈希值，如果两组数据非常相似，那么哈希值冲突的概率也越大，而冲突率是等于这两组数据的相似度的。当我们用Jaccard系数来计算用户点击历史的相似度时，这时的LSH就叫做MinHash。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们先来说明怎么为一个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"计算hash值，所有新闻集为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78c588fc149ffe8d6365f4b38665ad20.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们对集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78c588fc149ffe8d6365f4b38665ad20.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"进行一次随机置换，置换后的有序集合记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/783e3499179eb7972f407ce02bdd7027.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c3/c3ed9252758810d3cbfc729a687e788e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即一共有m+1条新闻)，我们计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/70dba63b692c08ac479eff5746efa59c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式表示的意思是，按顺序从左到右数，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中第一个包含在","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的元素的下标就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可以证明(有兴趣的读者可以自行证明，或者参考相关参考文献)，两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值冲突(值一样)的概率就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用Jaccard系数计算的相似度。所以我们可以将MinHash认为是一种概率聚类方法，对应的哈希值就是一个类：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d1efef6236f76e75d58e8797c2a937d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，所有哈希值为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e3/e3462e37dca54767653c18038dcb59c5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户聚为一类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c0/c037246f0e339da9457d218e2a3ac96e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个置换(即","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数)，将这","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数得到的哈希值拼接起来，那么两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个拼接的哈希值一样的概率就等于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/30/30411ed4e7b6aa17410657c916752ef6.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。很显然，通过将","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值拼接起来得到的聚类更精细(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值都相等的用户肯定更少，所以类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c0/c037246f0e339da9457d218e2a3ac96e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"更小，更精细)，并且相似度也会更高。从找用户最近的领域(最相似的用户)的角度来看，将","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值拼接起来的方法的精准度更高，但是召回率更低(聚类更小了，因此召回的新闻更少了，所以一般召回率就降低了)，为了提升召回率，获得更多的相似用户，我们可以将这个过程并行进行","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"次，最终每个用户获得","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个聚类，相当于进行了","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"次召回，在论文中作者建议","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取2到4，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取10到20。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在实际的工程实践上，由于新闻数量太大，进行置换操作耗时很大，可以采用简化的思路(精度会打折扣)，对于上面提到的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/380197618fcc8a3bbfd5149d990d281f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数(置换)，我们事先取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/380197618fcc8a3bbfd5149d990d281f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个独立的随机种子值与之一一对应，每个随机种子就是哈希函数的替代。对于每个新闻及每个种子值，我们利用该种子值和该新闻的Id(是整数值)，利用一个特定的哈希函数","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"计算出一个哈希值，该哈希值作为利用前面讲的通过置换后该新闻的下标，那么采用这种方法后用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希计算公式如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b4/b47522388ff3f85420baef58842e5d98.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法不需要对新闻集进行置换，会大大减少计算量，并且只要这个特定哈希函数","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的取值范围在0到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/24/2421b1f2e7bbd9d01aa35cd3998a08c6.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"之间，那么冲突概率就会比较小，通过这种近似的MinHash值与真正的MinHash值性质近似。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面讲解了MinHash聚类的算法实现细节，具体工程实现时是可以用Hadoop或者Spark等分布式计算平台来并行计算的，这里不细说。我们可以将每个用户的聚类及每个聚类包含的用户用倒排索引表的格式存储起来，方便后面做推荐时查阅。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6.2 基于聚类为用户做推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了用户的聚类，我们可以采用如下步骤来为单个用户生成个性化推荐，每个用户的推荐策略是一样的，所以可以采用分布式计算平台Spark等工具来并行化处理。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(1) 计算出用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(2) 计算出用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对所有新闻的评分","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(3) 将所有新闻评分降序排列，取topK作为该用户的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的(2)、(3)是非常简单的处理，我们重点来说一下(1)，怎么计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分。首先我们可以得到用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所属的所有类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/63/63cd7f3081339785220e1858f3cfd670.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，对于每个类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a37920d3e6468af62c1a9de73f258ea.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，取出该类别中所有的用户对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的点击次数之和(我们可以事先将每个类别中用户点击过的新闻及次数存储起来，方便查找)，再除以该类别所有点击之和，得到该类别对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分，那么用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所属的类别对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的总评分为：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9e/9e757ebf2053de8d667ded3ae9b61f30.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/be367d506b1ddaed3b24c5f833c7c66d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"即是刚刚提到的类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6f8d94c92537d44931e7c475aa400fa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中所有用户对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"点击次数之和，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c3/c347ed887b6aa2c83534e3cde1b3de49.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6f8d94c92537d44931e7c475aa400fa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有用户的所有点击次数之和。我们用上式计算出的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5f/5f9d6288735b7de534116ba9243f5cd5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"至此，基于作者自己的理解，简单介绍完了Google News基于用户聚类的推荐算法。该方法也只用到了用户及其他用户的新闻点击行为，因此也是一种协同过滤算法，该算法的细节读者可以阅读参考文献3。参考文献17、18、19、20有更多关于怎么用聚类来做推荐的算法，感兴趣的读者可以参考学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"总结","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本章讲解了关联规则、朴素贝叶斯、聚类等三类基础机器学习算法怎么用于个性化推荐的理论知识，同时从算法原理和工程实现的角度简单总结了YouTube和Google News的三篇分别采用关联规则、朴素贝叶斯、聚类思路来做推荐的论文。这几篇论文有很强的工程指导意义，值得读者学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"虽然这些算法原理简单、容易理解，看起来不那么高大上，但是这些算法却在工业界有过非常好的应用，在当时算是非常优秀的算法。这些算法现在可能看起来太简单了，也可能不会用在现在的推荐系统上，但它们朴素的思想下面蕴含的是深刻的道理，值得我们推荐从业者学习、思考、借鉴，希望读者可以很好地理解它们，并吸收这些朴素思想背后的精华。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"参考文献","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. The YouTube Video Recommendation System","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"2. Personalized News Recommendation Based on Click Behavior ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"3. Google news personalization: Scalable online collaborative flitering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"4. Robustness of collaborative recommendation based on association rule mining","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"5. Analysis of recommendation algorithms for e-commerce","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"6. Fast algorithms for mining association rules","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"7. Efficient adaptive-support association rule mining for recommender systems","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"8. Mining navigation history for recommendation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"9. Collaborative filtering by mining association rules from user acess sequences","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"10. Mining frequent patterns without candidate generation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"11. Pfp: parallel fp-growth for query recommendation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"12. Mining sequential patterns by pattern-growth: the PrefixSpan approach","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"13. Empirical analysis of predictive algorithms for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"14. A Bayesian model for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"15. Collaborative filtering with the simple Bayesian classifier","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"16. Probabilistic memory-based collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"17. Clustering methods for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"18. Rectree: A efficient collaborative filtering method","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"19. Scalable collaborative filtering using cluster-based smoothing","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"20. Latent class models for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]}]}
基于朴素ML思想的协同过滤算法（十七）
{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"写在前面：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"大家好，我是强哥，一个热爱分享的技术狂。目前已有 12 年大数据与AI相关项目经验， 10 年推荐系统研究及实践经验。平时喜欢读书、暴走和写作。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"业余时间专注于输出大数据、AI等相关文章，目前已经输出了40万字的推荐系统系列精品文章，今年 6 月底会出版「构建企业级推荐系统：算法、工程实现与案例分析」一书。如果这些文章能够帮助你快速入门，实现职场升职加薪，我将不胜欢喜。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"想要获得更多免费学习资料或内推信息，一定要看到文章最后喔。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"内推信息","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你正在看相关的招聘信息，请加我微信：liuq4360，我这里有很多内推资源等着你，欢迎投递简历。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"免费学习资料","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想获得更多免费的学习资料，请关注同名公众号【数据与智能】，输入“资料”即可！","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"学习交流群","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想找到组织，和大家一起学习成长，交流经验，也可以加入我们的学习成长群。群里有老司机带你飞，另有小哥哥、小姐姐等你来勾搭！加小姐姐微信：epsila，她会带你入群。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们在第十六章协同过滤推荐算法中介绍了经典的item-based协同过滤推荐算法。在本章中我们会继续介绍三种思路非常简单朴素的协同过滤算法，这几个算法的原理简单，容易理解，也易于工程实现，非常适合我们快速搭建推荐算法原型，并快速上线到真实业务场景中，作为其他更复杂算法的baseline，提供效果对比参考。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"具体来说，我们在本章中会介绍利用关联规则、朴素贝叶斯(naive bayes)、聚类三类机器学习算法来做协同过滤推荐的方法。并且还会介绍3个核心思想基于这三类机器学习算法的工业级推荐系统，这3个推荐系统被YouTube和Google分别用于视频和新闻推荐中(其中会介绍Google News的两个推荐算法)，这些算法在YouTube和Google News早期产品中得到采用，并且在当时情况下效果是非常不错的，值得我们深入了解和学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.1 基于关联规则的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"关联规则是数据挖掘领域非常经典的算法，该算法来源于一个真实的案例：“啤酒与尿布”的故事。该故事发生在20世纪90年代的美国沃尔玛超市中，沃尔玛的超市管理人员分析销售数据时发现了一个令人难以置信的现象：在某些特定的情况下，“啤酒”与“尿布”两件看上去毫无关系的商品会经常出现在同一个购物篮(用户一次购物所买的所有商品形象地称为一个购物篮)中，这种独特的销售现象引起了管理人员的注意，经过后续调查发现，这种现象出现在年轻的父亲身上。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在美国有婴儿的家庭中，一般是母亲在家中照看婴儿，年轻的父亲前去超市购买尿布。父亲在购买尿布的同时，往往会顺便为自己购买啤酒，这样就会出现啤酒与尿布这两件看上去毫不相干的商品经常会出现在同一个购物篮的现象。沃尔玛发现了这一独特的现象，开始在卖场尝试将啤酒与尿布摆放在相同的区域，让年轻的父亲可以方便地同时找到这两件商品，并很快地完成购物。这样做沃尔玛超市就让这些客户一次购买了两件商品、而不是一件，从而获得了很好的商品销售收入，这就是“啤酒与尿布”故事的由来。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我们给出关联规则的定义，假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/10/10f575e56de5600a4ae2d36db284fb2d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是所有标的物的集合(对于沃尔玛超市来说，就是所有的商品集合)。关联规则一般表示为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 的形式，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4c/4cb50d0ce11a7a10e9e835d0bf016326.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0b5e39df54538b7d3ff7ce20e1a254f8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的子集，并且","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/22/22079c0bfee2a2a89dd8dc1dd28fb877.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示如果","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在用户的购物篮中，那么用户有很大概率同时购买了","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。通过定义关联规则的度量指标，一些常用的关联规则算法(如Apriori)能够自动地发现所有关联规则。关联规则的度量指标主要有","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"支持度(support)","attrs":{}},{"type":"text","text":"和","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"置信度(confidence)","attrs":{}},{"type":"text","text":"两个，支持度是指所有的购物篮中包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/33/33db192393da378bb603f67324899e66.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的购物篮的比例(即","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4c/4cb50d0ce11a7a10e9e835d0bf016326.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同时出现在一次交易中的概率)，而置信度是指包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的购物篮中同时也包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例(即在","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"给定的情况下，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"出现的条件概率)。它们的定义如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78de2f5125aec1dbe8288636c7a6e8e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5e/5e31009ad08de2759fefb954d787c148.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"支持度越大，包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/33/33db192393da378bb603f67324899e66.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的交易样本越多，说明关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有更多的样本来支撑，“证据”更加充分。置信度越大，我们更有把握从包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的交易中推断出该交易也包含","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。关联规则挖掘中，我们需要挖掘出支持度和置信度大于某个阈值的关联规则，这样的关联规则才更可信，更有说服力，泛化能力也更强。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了关联规则的定义，下面我们来讲解怎么将关联规则用于个性化推荐中。对于推荐系统来说，一个购物篮即是用户操作过的所有标的物的集合。关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示的意思是：如果用户操作过","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b1433559f8344f0ea6e284db52323d90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的所有标的物，那么用户很可能喜欢","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的标的物。有了这些说明，那么利用关联规则为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"生成推荐的算法流程如下(假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有操作过的标的物集合为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f5/f5fde0280c0e5db9eadae1c57b8a4807.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 挖掘出所有满足一定支持度和置信度(支持度和置信度大于某个常数)的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"2. 从1中所有的关联规则中筛选出所有满足","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9d/9d52f7f4f737c9f9057b3d90c47d6fd7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"3. 为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"生成推荐候选集，具体计算如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ff/ffa3896025e7ce0a4a1b3dd814e1ade7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"即将所有满足2的关联规则","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/35/3566e0fc5849bf365b05677630af9eb5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bee4525663d975427bff2f1baa2ae.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"合并，并剔除掉用户已经操作过的标的物，这些标的物就是待推荐给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的。对于3中的候选推荐集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，可以按照该标的物所在关联规则的置信度的大小降序排列，对于多个关联规则生成同样的候选推荐标的物的，可以用置信度最大的那个关联规则的置信度。除了可以采用置信度外，也可以用支持度和置信度的乘积作为排序依据。对于4中排序好的标的物，可以取topN作为推荐给用户的推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于关联规则的推荐算法思路非常简单朴素，算法也易于实现，Spark Mllib中有关联规则的两种分布式实现","attrs":{}},{"type":"link","attrs":{"href":"http://spark.apache.org/docs/latest/ml-frequent-pattern-mining.html#fp-growth","title":null,"type":null},"content":[{"type":"text","marks":[{"type":"underline","attrs":{}}],"text":"FP-Growth","attrs":{}}]},{"type":"text","text":"和","attrs":{}},{"type":"link","attrs":{"href":"http://spark.apache.org/docs/latest/ml-frequent-pattern-mining.html#prefixspan","title":null,"type":null},"content":[{"type":"text","marks":[{"type":"underline","attrs":{}}],"text":"PrefixSpan","attrs":{}}]},{"type":"text","text":"，大家可以直接拿来使用(关于这两个关联规则挖掘算法的实现细节，读者可以阅读参考文献10、11、12)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"关于关联规则算法的介绍及怎么利用关联规则进行个性化推荐，读者还可以阅读参考文献4、5、6、7、8、9。利用关联规则做推荐，是从用户的过往行为中挖掘用户的行为模式，并用于推荐，只用到了用户的行为数据，因此利用关联规则做推荐也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.2 基于naive bayes的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"利用概率方法来构建算法模型为用户做推荐，可以将预测评分问题看成一个分类问题，将可能的评分离散化为有限个离散值(比如1、2、3、4、5一共5个可行的分值)，那么预测用户对某个标的物的评分，就转化为用户在该标的物上的分类了(比如分为1、2、3、4、5个类别，这里不考虑不同类之间的有序关系)。在本节我们就利用最简单的贝叶斯分类器来进行个性化推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假设一共有k个不同的预测评分，我们记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d029b3077eaeaa602828adf1bdcd4fe4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，所有用户对标的物的评分构成用户行为矩阵","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/28/28c0efcd8cb2b85b45a681ad5deddcb1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，该矩阵的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0bca50881ea2309ffeb904896030f691.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"-元素记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/556ff0654442219f13cff874fc33f776.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即是用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/27/2747df64c9962eabc30e110288bc1af5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分，取值为评分集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的某个元素。下面我们来讲解怎么利用贝叶斯公式来为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"做推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假设用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有过评分的所有标的物记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e4/e4ba2d2682f317d2142fe6060f88eaac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。现在我们需要预测用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对未评分的标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/77/77e88c3b80690657e3f48a5e21d1575c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")。我们可以将这个过程理解为在用户已经有评分记录","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的条件下，用户对新标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中某个值的条件概率：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"条件概率","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/06eb881946e17f1c4eaa4285dd13215c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，表示的是在事件","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a7860bd927513eb3e3e59b48de9ee2d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"发生的情况下事件","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f5/f5fde0280c0e5db9eadae1c57b8a4807.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"发生的概率，由著名的贝叶斯定理，条件概率可以通过如下公式来计算：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3898ed74b47c0813d9bb195f6cf62990.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因此，回到我们的推荐问题，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce13daa025667649f6edda548ccd06d1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/62/622a18b91784d956935c3742052c3fde.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们需要确定具体的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"值，让上式左边的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值最大，这个最大的值","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8f/8f2ebdc872d90ebd7810f31ebdd451a5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就可以作为用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对未评分的标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d8/d8c301b61fcad4679dc43b1b4b4b0ce3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"=","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8f/8f2ebdc872d90ebd7810f31ebdd451a5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")。我们注意到上式中右边的分母的值与具体的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"无关，因此右边分子的值的大小才最终决定公式左边的值的相对大小，基于该观察，我们可以将上式记为：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3efdf0f90bea89611d96e597acfa4559.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"现在的问题就是怎么估计上式右边项的值，实际上基于用户评分矩阵，这些项的值是比较容易估计出来的，下面我们就来估计这些值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其实是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1de4ba7abadcf5360e6fc1db76f482c3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的先验概率，我们可以用对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户的比例来估计该值，即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/61098f16b42a2980e5aa589873d89ed5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里分母是所有对标的物","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有过评分的用户，而分子是对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"要估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们需要做一个朴素的假设，即条件无关性假设：用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有的评分","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1e/1e2e97763facf19ed7c34f0f821d0317.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是独立无关的，也就是不同的评分之间是没有关联的，互不影响(该假设就是该算法叫做naive bayes的由来)。实际上，同一用户对不同标的物评分可能是有一定关联的，在这里做这个假设是为了计算方便，在实际使用naive bayes做推荐时效果还是很不错的，泛化能力也可以。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了条件无关性假设，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就可以用如下公式来估计了：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2b/2b23cb81a4f7e39ab34e3290dff9caf8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/69/69c43e39d282f5bacccdd2c71f1273f5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可用所有对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户中对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/62/625fe11fcdfe277ff5ee1e0b82e51ae3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ec/ecc054779d194a4f806b7a33a42ac988.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例来估计。即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ca/ca01a319b0ef24ec70f044226b65f439.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面的两个估计，那么我们利用naive bayes计算用户对标的物的评分概率问题最终可以表示为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ec/ec24965db859ecf9a5f18c5f1c7f783e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"size","attrs":{"size":10}}],"text":"公式1：用户对标的物评分的概率估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上式，一般来说，我们可以采用两种方法来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8d/8dd0a304c30df6acb81f0e3e787506e2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. 类似极大似然的思路估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法就是用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2e/2ed42750f5567ea3d4a7cabe24ded447.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，使得","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取值最大的p对应的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49b92b1a44586741899b90b9f37d2c46.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"作为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1de4ba7abadcf5360e6fc1db76f482c3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计值，即","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/31/31a5aa93a34cf906d94faac1349d0f90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法仅仅将用户对标的物的评分看为类别变量而忽略具体评分的数值，而下面的方法则利用了评分的具体数值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"采用加权平均来估计","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/54/544a2986a44e691e0a184a1119e9702e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef3aefc8da69c0f667da6d02060ffd86.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可以取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ca/cabe5d856a72918812ec4217c941a41f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的任一值，基于上面的公式1，取每一个值都有一个概率估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a939807f1bf2d8b0622af90df682e120.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么最自然的方式是可以用这个概率作为权重，利用加权平均来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c8/c8330daacddda7697f407fa297ba1b34.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，具体的估计公式如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4a/4af511d78ae35989431d639c6a41bc1a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了用户对标的物评分的估计，那么推荐就是顺其自然的事情了。具体来说，我们可以计算出用户对所有未评分标的物的估计值，再按照估计值的大小降序取topK作为给用户的推荐。这里说明一下，对于采用极大似然思路的估计(即上面的第一种估计方法)，因为该方法是将评分看成类别变量，那么肯定有很多标的物的估计值是一样的，这时如果我们需要再区别这些评分一样的标的物的话，可以采用估计该值时的概率大小再进行二次排序。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"采用贝叶斯方法来做推荐会存在一些问题，具体来说，我们在估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"和估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，由于样本数据稀疏，导致无法进行估计或者估计值不够鲁棒性的问题。比如在估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7d75c3000a6dde158794734702e96854.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，我们用公式","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/61098f16b42a2980e5aa589873d89ed5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来估计，从该式可以看到，如果无用户或者很少用户对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有评分(这种情况是存在的，如","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是新加入的标的物或者是冷门标的物)，这时可能会出现用 ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dd/dd878cc6534016e300a2742223eef033.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 来估计的情况，即使不是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dd/dd878cc6534016e300a2742223eef033.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，当分子分母都很小时，估计值波动会很大，不够鲁棒，对估计结果影响很大。一般我们可以采用拉普拉斯平滑(Laplacian smoothing)的方法来处理，得到更加稳定的估计值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"针对上面这个例子，我们来说下怎么利用拉普拉斯平滑来处理：假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1d/1da0a3e6e3bfe1044f786ab028e19ced.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评分分别为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e8/e8c3e3f48b063dc75a8f817d23f49ad1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户数，那么上面的估计就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/36/36f57954ec3eac5a20523f56ce7646d3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"增加拉普拉斯平滑后的估计公式就是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b1/b17af01eba0bb80f0e645ae8e969b7dc.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从这个公式可以看出，当没有用户对标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/81832e39a2aa788a8c71f4cc5687d095.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"评过分时，就用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3ed596c8138fe9b87243fdbd1e4d74b7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来估计，这是在没有已知信息的情况下比较合理的估计。上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/075b484a80fde9e9a75b3cdf599af16d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是光滑化因子，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/075b484a80fde9e9a75b3cdf599af16d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"值越大，估计越光滑(鲁棒性越好)，这时公式对数据就不够敏感。对于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/3885c3602fd3e8ce2081110eff2cf288.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的估计，也可以采用一样的方法，这里不再赘述。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到此为止，我们讲完了怎么利用naive bayes来为用户做推荐的方法，该方法也是只利用了用户的操作行为矩阵，所以也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"naive bayes方法是一个非常简单直观的方法，工程实现也非常容易，也易于并行化。它对噪音有一定的“免疫力”，不太会受到个别评分不准的影响，并且也不易于过拟合(个人觉得前面介绍的条件无关性假设是泛化能力强的主要原因)，一般情况下预测效果还不错，并且当用户行为不多时，也可以使用(需要利用拉普拉斯平滑来处理)，而不像矩阵分解等算法，需要大量的用户行为才能进行推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"读者可以从从参考文献13、14、15、16中了解更多关于怎么利用贝叶斯及其他概率方法来做推荐的方案。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3 基于聚类的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于聚类来做推荐有两种可行的方案，一种是将用户聚类，另外一种是将标的物聚类。下面来简单描述一下怎么基于这两种聚类来做推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3.1 基于用户聚类的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果我们将所有用户聚类了，就可以将该用户所在类别的其他用户操作过的标的物(但是该用户没有操作行为)推荐给该用户。具体计算公式如下，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f8/f8a96beda26f47dfeeeeda787343463e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是给用户u的推荐，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户所在的聚类，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ac/ac34fa6802ecef1ad881eb76e49141fc.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4b/4b49d6e8dfe81bc88d07f5c21ee003e7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"分别是用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a7/a782d6c46919465c474437c36468ccbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的操作历史集合。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a4/a4ea8cc28805ac4e769fdf17a77d0402.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么怎么对用户聚类呢？可行的方案主要有如下几类：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(1) 基于用户的人口统计学特征对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用户的年龄、性别、地域、家庭组成、学历、收入等信息都可以作为一个特征，类别特征可以采用one-hot编码，所有特征最终都可以转化为数值的，最终获得用户特征的向量表示，通过Kmeans聚类算法来对用户聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 基于用户行为对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"比如采用矩阵分解就可以获得用户的嵌入表示，用户操作行为矩阵的行向量也是用户的一种向量表示，再利用Kmeans对用户进行聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(3) 基于社交关系对用户聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果是社交产品，用户之间的社交链条可以构成一个用户关系图，该社交图中所有的联通区域就形成了用户的一种聚类。这种推荐其实就是将你的好友喜欢的标的物推荐给你。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.3.2 基于标的物聚类的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果有了标的物的聚类，推荐就好办了。从用户历史行为中的标的物所在的类别挑选用户没有操作行为的标的物推荐给该用户，这种推荐方式是非常直观自然的。具体计算公式如下，其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f8/f8a96beda26f47dfeeeeda787343463e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的推荐，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7b/7b407c68ca521579f54061f76b81cf0e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户的历史操作行为集合，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a0e7d428c6c5baa7549f6f597f2426f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是标的物","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所在的聚类。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8e/8ea259bd8eb4f2246a4e99ecf0165195.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同时，有了标的物聚类，我们还可以做标的物关联标的物的关联推荐，具体做法是将标的物A所在类别中的其他标的物作为关联推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么怎么对标的物聚类呢？可行的方法有利用标的物的metadata信息，采用TF-IDF、LDA、Word2vec等方式获得标的物的向量表示，再利用Kmeans聚类。具体的实现细节这里不介绍，感兴趣的读者可以自行搜索相关材料做深入学习，作者在第五章《基于内容的推荐算法》中也做了比较详细的介绍。另外，也可以基于用户的历史操作行为，获得标的物的嵌入表示(矩阵分解、item2vec等算法)，用户行为矩阵的列向量也是标的物的一种向量表示。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"参考文献17、18、19、20有更多关于怎么用聚类来做推荐的算法，感兴趣的读者可以参考学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到此为止，我们讲完了基于关联规则、naive bayes、聚类做个性化推荐的方法。下面我们就基于这几个方法的思想来介绍三个工业级的推荐引擎，供大家学习参考，同时也希望借助这几个工业级推荐系统的介绍让大家加深对这三个方法的思路的理解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4 YouTube基于关联规则思路的视频推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"YouTube基于关联规则思路的视频推荐算法(见参考文献1)建立在一个基本假设基础之上：如果用户喜欢种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么用户喜欢与种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"相似的候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率一定很大，候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越相似，那么用户喜欢候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率也越大。那么剩下就是怎么解决这两个问题了：一是怎么计算两个视频的相似度，二是怎么选择种子视频，下面我们来分别介绍。同时，我们也会介绍最终怎么给用户生成个性化推荐。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.1 计算两个视频的相似度(关联度)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该算法是利用关联规则的思路，在一定时间内(比如24小时内)统计两两被用户同时播放过的视频对","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/bea12e797c1b852eb00b88566fcf8da1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，将播放次数计为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/aa/aa34d8d2b59d55b38278e7e65e5474d0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度可以表示如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e7/e7042221e3714874fc5823af015ea028.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f6/f6b74fcb97d71ceab7c15fcb8ef198e8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是一个归一化常数，会综合考虑种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的“全局流行度”，如果我们分别记","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"、","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在上面的一段时间内总的播放次数。那么我们可以定义","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/61/6197d9d468abc64e08c41b3b1a31f7b5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该归一化函数是非常直观简单的，用其他归一化函数也是可以的。如果用该归一化函数的话，对所有候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来说，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是一样的，所以可以忽略，其实我们是用候选视频的“全局流行度”","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来归一化。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在分母中，这说明","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ea/eaac4ca97c4e94546d139327bd5b557e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越大的视频，与种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度会更小，该归一化方法更加偏向于偏冷门的候选视频。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面只是一个非常简单的描述和计算公式，我们也可以将视频的metadata、观看时间等信息整合进来计算相似度。另外，还需要处理脏的播放行为数据。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.2 基於单个种子视频生成候选视频集","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于相似度计算公式","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c11ca2ccbf9c889ba0fe64dd0c5fe4d8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们可以选择出种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的最相似的topN候选集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a2/a22a20d87fbb62ee9267b46cb32b9dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，一般我们会确定一个最小的阈值，需要相似度大于该阈值才会选出来，这也是为了避免选择很多只有很少播放量的视频(这时种子视频和候选视频被同时播放的次数也很小)导致推荐结果太差。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于上述从种子视频选择候选视频的规则，我们可以构建一个有向图。将所有视频集合构成一个有向图，对于任何一个视频对","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/bea12e797c1b852eb00b88566fcf8da1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，如果","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a9/a9a82d14a60740e96d8daffbf93430be.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似视频列表集中)，那么存在一条从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的边，边的权重为这两个视频的相似度","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c11ca2ccbf9c889ba0fe64dd0c5fe4d8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"利用该方式为种子视频生成的视频候选集，可以作为视频的关联推荐，为种子视频推荐相关的视频。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.3 基于用户行为为用户生成推荐候选集","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面讲到了单个视频怎么生成候选集，那么对於单个用户也是很容易采用上面的方式生成推荐候选集的。我们可以将用户播放过的视频或者明确表示过喜欢的视频作为初始种子视频集。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于初始种子集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们可以采用如下方式来生成候选集：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于上面视频的有向图解释，我们可以沿着集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的有向边向外拓展，对于任意的种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2f/2fd82b8b38d3a5bffa54ce6929085c8d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，我们考虑它的相关视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a2/a22a20d87fbb62ee9267b46cb32b9dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。我们将所有通过这种方式拓展出的视频集记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，那么我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/49/49fab68263c5ad4a9db908b14cb62abb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"一般情况下，我们计算出","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就足够获得比较多的、效果还可以的、有一定多样性的推荐候选集了。但实际上，通过这种方式生成的推荐候选集种类比较狭窄，跟用户的兴趣太相似。这种方式虽然生成了用户可能感兴趣的视频，但是可能用户没有太多惊喜，会让用户沉浸在比较小的视频范围内，就像进入了一个漩涡中，无法发现更大更精彩的世界。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为了拓展用户的候选推荐集的空间，解决上述越推越窄的问题，我们可以沿着种子视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所在的视频有向图进行n次向外拓展(用图论的术语，就是n次传递闭包)，我们记","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/01/018e89b840196237917dd30cee1df40a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为通过种子集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的某个种子视频通过不超过n次路由可达的所有视频组成的集合，那么我们有","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c2/c2b222ec07f1ec1777b7c95e978fe48e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"注意，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/26/2610cbb553a884e23fca6e4ab0b60808.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，上面的公式也跟前面提到的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/063f17cebc4cb7b182738b10e232ebac.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的公式是兼容的。那么我们最终生成的推荐候选集就是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2a/2a27fba5c3fc7920462fc728ac918662.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"一般N很小(拓展很少的几步)时就可以获得非常多具备多样性的推荐结果，即使对种子集很小的用户也是如此。通过上述路径拓展，我们可以为每个候选的推荐视频关联一个种子视频(通过上述拓展，从某个种子视频到候选视频的路径就将候选视频关联到了种子视频)，该种子视频既可用于后面的推荐结果排序，还可以作为推荐解释(例如如果候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"获得的，我们可以用“因为你喜欢/看过","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"”来作为推荐解释语，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7dae360e30c2ae88e8361579fd5c5def.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c16b999355de919ec6c68f83f14be424.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过多步相似链接在一起的，它们多少是有一些相似性的，用户从这两个视频中是可以直接感知到这种相似的，所以该推荐理由是有一定说服力的)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.4.4 推荐结果排序","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过上面7.4.3中的介绍，我们可以为用户生成推荐候选集了，那么这些候选集中的视频怎么推荐给用户呢？也即我们怎么对这些候选视频排序呢？我们需要将用户更愿意点击的排在前面。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以从视频质量、用户对视频的偏好度、多样性等几个维度来考虑。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"视频质量是指视频本身的吸引力，比如视频的海报清晰度、视频播放次数、视频被点赞的次数、视频被转载的次数、视频被收藏的次数等。这些不同维度的视频质量，我们可以通过打分获得一个固定的质量得分，具体打分方式可以多种多样，这里不再细说。我们这里记视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/111d380bcea903d6659fe965616f0437.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的质量为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/707b45b3dc6a33ba782451de2d519dab.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过前面的介绍我们知道每个候选视频是通过某个种子沿着有向图通过若干步的拓展获得的。如下图，假设候选视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是通过种子视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"经过k步获得，下图中箭头上方的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9b/9bb641d69bf9e8227258e729b2a1da04.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是相邻两个视频的相似度。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/077b1cf3171fba200dfcfb395aa0364a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"那么用户对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的偏好度可以用如下公式来计算","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b69f24666a4b38ced3309c25546cbf94.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其中，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7c/7c188113708f2be571f40f1437fa899b.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的偏好度及它自身的受欢迎程度，我们可以通过用户播放","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的时长或者","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"总播放量等数值来度量。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/79/79df767e5ca7d65ab529e4f68bf49dbf.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有多条路径，可以选择最短的路径，这是因为我们是一步一步拓展获取候选集的，当某个视频被某一步拓展到了，后面再拓展到它时，前面已经计算了，所以在这一步就忽略掉。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面介绍的候选视频得分及用户对视频的偏好度，我们可以用下面公式来计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对视频","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/39/3904351a36189360ba84adf76d22ec27.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最终的评分：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0b/0bc0ba7fe13c692e042dd73de61f8bc4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过将所有候选视频按照上述公式降序排列就可以得到候选视频的排序了。利用上面公式，距离用户种子视频集","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/42/42f8e3d68f11b2c7306caa8e49b72efe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"越远，通过公式","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3e/3e93f2d033b09d3e1e66b8f6eec41281.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 的相似性连乘得到的值也越小，那么就有可能排在后面了。那么我们怎样解决这个问题获得多样性呢？一般我们可以通过限制由同一种子视频生成的候选视频的数量来获得多样性(因为同一种子视频生成的视频多少是有一些相似度的)，或者限制由同一渠道产生视频数量(比如由同一个用户上传的视频)。通过在上述排好序的推荐列表中，剔除掉部分由同一种子视频生成的视频或者同一渠道产生的视频，就可以获得最终的推荐结果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面介绍的就是YouTube基于视频被用户共同观看的次数获得视频之间的相似度，进而通过视频相似度传递获得最终推荐的方法。该方法本质上就是关联规则的思路，只用到了用户的播放行为信息，因此也是一种协同过滤算法。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5 Google News基于贝叶斯框架的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前面7.2节简单讲了怎么利用naive bayes算法来为用户生成个性化推荐的一般思路，在这一节我们讲解Google News利用贝叶斯框架来做推荐的具体方法。Google的这篇文章(参考文献2)采用另外的思路，基于用户过去看新闻的历史行为利用贝叶斯框架来预测用户当前对新闻的兴趣，再结合协同过滤来做推荐。下面我们来讲解该篇文章的核心思想。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.1 基于用户过去的行为来分析用户的兴趣点","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先将所有新闻按照事先确定好的类别分成若干类(主题)：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ef/ef9bc778a25c30535de42dc87abe5ebe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，如“世界”、“体育”、“娱乐”等类别。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先计算某个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在某段时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(比如按照一个月一个周期等)内的点击行为在上述类别上的分布，记为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d0af070680a56f3bd97ef511923f92b5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式1：用户u在时间周期t内的行为在新闻主题上的分布","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/01/0164404b5bc457d4ef358b6d1e96a89b.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"代表用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内点击主题类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的次数。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d4/d4a7f7490f4f0106d5152202f097afaa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是该用户在这段时间周期内点击新闻的总数量。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内在各个新闻主题类别上的时间花费分布，反映了用户的兴趣分布。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"新闻是有地域差异性的，同样地，类似单个用户的兴趣偏好分布，我们可以统计某个国家或者某个地区的所有用户点击行为的整体在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内在上述新闻主题上的分布。我们将该分布记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。计算方法和上面单个用户一样，将该国家或地区所有用户当成一个整体来计算。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该文章通过大量的数据分析，最终得到如下4个结论，后面的贝叶斯框架也是基于这几个结论来展开的。细节的分析读者可以阅读参考文献2。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(1) 用户的兴趣确实随着时间变化；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(2) 公众对新闻的点击分布反映了兴趣的发展趋势，并受到重大事件(如世界杯等)的影响；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(3) 不同国家/地区对新闻的偏好是不一样的，存在不同的发展趋势；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(4) 从某种程度上说，单个用户的兴趣变化趋势是受到该用户所在国家/地区的新闻趋势变化影响的；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了上面的基本概念和初步数据分析得到的结论作为基础，下面我们来说明怎么用贝叶斯框架来为用户的兴趣建模。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.2 利用贝叶斯框架来建模用户的兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以将用户的兴趣分为两种：一种是用户的真实兴趣，一种是会受到国家/地区大的兴趣趋势影响的临时兴趣。用户的真实兴趣是由用户的性别、年龄、受教育程度、专业等决定的，它是相对稳定的，不太会随着时间而急剧变化。另一方面，当用户觉得要读什么新闻时，是会受到用户所在区域新闻趋势的影响的，这种影响是短期的，是随着时间变化的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"基于用户点击行为模式和用户所在地群体的行为模式，可以通过贝叶斯框架很好地预测用户当前对新闻的兴趣，具体可以通过如下三个步骤来获得用户的当前兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(1) 预测用户在某个时间周期内的真正兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于特定时间周期","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内的某个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ce/ce518b8a1c9c6904fabfef47edade938.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户在所有新闻主题上的点击分布，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户所在地域整体用户的兴趣分布，代表的是兴趣趋势。我们期望学习用户的从","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"呈现出的而不会受到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"干扰的真实兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示用户在新闻主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上的真实兴趣，它是一个条件概率，表示在新闻主题为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的条件下，用户进行点击的概率。利用贝叶斯公式，我们可以采用下式来计算","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/41/4121995498205c1ab1b3b12ff91f7316.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式2：用户点击属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的文章的概率","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/07/0740d669ce82a10b7d284aa48a739a8d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户点击的所有新闻中该新闻属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的概率，它可以从用户的点击分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中估算出(参见上面的公式1，可以用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9909d542f9674d761fbf8bef9b4140e1.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的第i个分量来估算)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d935e80c2453c95b6fb816aeec86dbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是新闻属于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的先验概率，也就是在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内所有发布的新闻属于类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的比例，它与用户所在地域的新闻变化趋势相关，如有有更多的有关主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的新闻事件发生，那么关于主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的新闻就会越多。我们可以用整体分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c9/c9fce73c2cc61b598f10061ae92efd89.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的第i个分量来近似估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d935e80c2453c95b6fb816aeec86dbe.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5c/5c8140b53c9fc6345448b8880c400615.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户点击任何一个类别的文章的先验概率，与具体的文章主题无关。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从上面公式2知道，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/06/0695d31b4e03595312f1ccd971a13227.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"表示用户对主题","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的感兴趣程度，不同于该地区其他用户的兴趣。如果用户读了很多体育类的新闻，而很多其他用户也读了体育类新闻，这可能是有一些体育相关热点事件引起的。相反，如果该用户阅读了大量体育新闻而该地区其他用户很少读体育新闻，这就代表的是用户真的对体育感兴趣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 结合用户在不同时间周期的兴趣，获得用户精确的与时间无关的真实兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面(1)中计算了用户在一个时间周期","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内的兴趣偏好，我们可以将用户在过去统计周期内所有时间周期的兴趣归并起来获得用户综合的对新闻类别的真实兴趣偏好，具体参见下面公式的计算逻辑。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4e/4e899406ddcadbe9fd235c04722cc997.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4e/4e899406ddcadbe9fd235c04722cc997.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9e/9eb5f16df9d10f8e4d32386603a6d40a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用户在时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"内总的新闻播放量。我们可以假设用户在所有时间周期内点击一篇新闻的先验概率是固定不变的，也即假设上式中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c4/c4d882f2951d4d3a496f6cee5f2e7aa7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"与时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"无关，我们记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e1/e13042d36dcba643f2b7aa9088284e70.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。那么上式可以改写为下面的","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/65/65c2312ac858017017b80f30f48e0318.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式3：用户在过去统计周期内所有时间段的综合兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的公式3就是用户的真实兴趣，该兴趣其实是用户在多个时间周期内的兴趣的某种加权平均。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(3) 结合用户真实兴趣和当前的新闻趋势，预测用户当前的兴趣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如前面所说，用户的兴趣可以分解为两部分，一部分是用户长期的的真实兴趣，另外一部分是受到当前趋势影响的短期兴趣。(1)、(2)基于用户过去的点击播放行为计算出了用户的长期的真实兴趣。为了度量用户当前对新闻的短期兴趣，我们用用户所在地域的所有用户在一个较短时间段(比如过去一个小时)的整体点击分布来刻画(用","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/29/299165c09284ff58330d00b0bf4b52c4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示)，由于所在地域有大量用户，在这段较短时间内也有足够多的数据来准确计算出哪些新闻主题是热门的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们的最终目标是预测用户在将来一段时间的点击分布，同样地，我们可以用贝叶斯公式得到下面的计算公式：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/09/09de797bfbe6b86428104f17d948b95c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们用用户的真实兴趣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e0/e0426b9e90d0468cedbdc10677ae64c2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(公式3)来估计","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dc/dc087d2a66753eef9635cacebe1cadb3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，并且假设用户点击任何一篇新闻的概率为常数，不受时间影响(即假设","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/10/1055dd12983b5c06d0e8bdf6494d4b25.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"=","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e7/e75c70ea57b3aaee155253f91d8819fb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，那么上式就可以表示为(将公式3代入进来)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d4/d418d08d9bc8ae7abde252fc36ff54f4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以在上式中加上一个虚拟点击项，它跟当前新闻趋势的概率分布","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c1/c134c11f0e434d95c65752cd9fb109f5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同分布，那么用户在未来短时间内对新闻的兴趣偏好概率最终变为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7a/7a908144ca516e687940fd02d131a03f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"公式4：用户当前对新闻主题的兴趣偏好概率","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式中的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就是虚拟点击数(在参考文献2中取值为10)，它可以看成是一个光滑化的因子，当某个用户只有非常少的点击历史时，这时是用户当前的新闻趋势(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/ee/ee3477f4ce71893a8d1f766b3d993219.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")来预估该用户的点击概率，这在没有太多该用户历史数据的情况下是一个合理的估计。当","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7c/7c7a7b79351ff3c51248d98ccc9ae79c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"远远大于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"时，上式就可以忽略","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2a688087c1d85aec102e6fee7fb6d0f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，还原为用户真实的点击分布预估。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上述预估用户将来短时间内的兴趣分布的方法的一个重要优点是，我们可以增量地计算用户的点击分布。我们可以将过去每个时间周期","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/11e8aca6190029b09993a8df73cdd04f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对应的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6feb409afa05e093607793382d8241c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"和","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6f/6fbb66310067cb02f2beed3e6a4b4cd7.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值事先存起来，当更新用户的兴趣偏好概率时，只需要将最近一个时间周期的值计算出，利用上面的公司4及预先存下来的过去时间段的值就可以得到用户最新的兴趣偏好分布。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.5.3 为用户做个性化推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"为了对推荐候选集进行排序获得最终的推荐结果，该推荐算法计算出两个统计量：一个是","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d1/d1fff0932d64af440746e1f69233870c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，称之为信息过滤得分，另外一个是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/8146c5fa738688e3cc99a6490bd283d0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即协同过滤得分(利用协同过滤算法预测的用户对新闻的得分，可以利用参考文献3中的方法得到)。其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的计算过程是这样的，先获得该文章的类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，再基于上面的公式4得到用户对类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6d/6d458838d5589376c044e8710db4b163.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的的偏好概率，该值作为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1a/1acd5c87caa2fb38fbf2a3f0226a3729.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的值。我们将这两个得分相乘，最终利用如下的公式来计算用户对某个新闻的兴趣得分。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b5/b5afc00e35e230005f2f83d811cc3ef3.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最终基于上述公式计算出该用户对所有新闻的得分，取得分最高的topN作为最终的推荐结果。该方法通过在Google news上验证，比单独采用协同过滤有更好的预测效果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法利用用户过去及用户所在地区的点击行为来预测用户当前对新闻的偏好概率，再与协同过滤结合进行最终的推荐。预测用户兴趣偏好概率的过程只用到了用户及用户所在地域全体用户对新闻的点击数据，因此也是一种协同过滤方法。细节的实现方案，读者可以阅读参考文献2进行进一步了解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6 Google News基于用户聚类的推荐算法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"参考文献3中利用了3种模型来预估一个用户对一个新闻的评分，最终通过加权平均获得用户对新闻的最终评分，其中第三种方法covisitation的思想我们在第6章《协同过滤推荐算法》第6节“近实时协同过滤算法的工程实现“有详细讲解，本质上是一种关联规则的思路，我们这里不再介绍。另外两种算法分别是基于MinHash和PLSI聚类的方法，在这里我们只介绍MinHash算法，PLSI算法读者可以自行阅读参考文献3来了解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6.1 基于MinHash聚类","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对于用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，他的点击历史记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。那么两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/83/83420fe338ed63e05e679d085981a8e0.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的相似度可以用Jaccard系数来表示：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f1/f1d9daa149033398ec80d1f65ecc1b87.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了两个用户之间的相似度，我们可以非常形式化地将相似用户点击过的新闻通过上面的相似度加权推荐给用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。但是用户数和新闻数都是天文数字，无法在极短时间内为大量用户完成计算。这时，我们可以采用LSH(","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"L","attrs":{}},{"type":"text","text":"ocality ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"S","attrs":{}},{"type":"text","text":"ensitive ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"H","attrs":{}},{"type":"text","text":"ashing)的思路来计算，大大减少计算复杂度。LSH的核心思想是，对于一组数据(对于我们这个场景来说，这一组数据就是用户的历史点击记录","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":")，我们可以用一组哈希函数来获得哈希值，如果两组数据非常相似，那么哈希值冲突的概率也越大，而冲突率是等于这两组数据的相似度的。当我们用Jaccard系数来计算用户点击历史的相似度时，这时的LSH就叫做MinHash。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们先来说明怎么为一个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"计算hash值，所有新闻集为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78c588fc149ffe8d6365f4b38665ad20.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，我们对集合","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/78c588fc149ffe8d6365f4b38665ad20.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"进行一次随机置换，置换后的有序集合记为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/78/783e3499179eb7972f407ce02bdd7027.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c3/c3ed9252758810d3cbfc729a687e788e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，即一共有m+1条新闻)，我们计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值为","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/70dba63b692c08ac479eff5746efa59c.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上式表示的意思是，按顺序从左到右数，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中第一个包含在","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b7/b780870e063041266d218b631d7f52f9.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中的元素的下标就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"可以证明(有兴趣的读者可以自行证明，或者参考相关参考文献)，两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希值冲突(值一样)的概率就是","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用Jaccard系数计算的相似度。所以我们可以将MinHash认为是一种概率聚类方法，对应的哈希值就是一个类：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5d/5d1efef6236f76e75d58e8797c2a937d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，所有哈希值为","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e3/e3462e37dca54767653c18038dcb59c5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的用户聚为一类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c0/c037246f0e339da9457d218e2a3ac96e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个置换(即","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数)，将这","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数得到的哈希值拼接起来，那么两个用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/90/9074ce89113e8f747f12edbab4c27bbb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个拼接的哈希值一样的概率就等于","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/30/30411ed4e7b6aa17410657c916752ef6.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"。很显然，通过将","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值拼接起来得到的聚类更精细(","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值都相等的用户肯定更少，所以类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c0/c037246f0e339da9457d218e2a3ac96e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"更小，更精细)，并且相似度也会更高。从找用户最近的领域(最相似的用户)的角度来看，将","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希值拼接起来的方法的精准度更高，但是召回率更低(聚类更小了，因此召回的新闻更少了，所以一般召回率就降低了)，为了提升召回率，获得更多的相似用户，我们可以将这个过程并行进行","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"次，最终每个用户获得","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个聚类，相当于进行了","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"次召回，在论文中作者建议","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fb/fb86115033b583781e510ad42aa24bec.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取2到4，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fc/fcde43a58f0f99371169978b01097a80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"取10到20。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在实际的工程实践上，由于新闻数量太大，进行置换操作耗时很大，可以采用简化的思路(精度会打折扣)，对于上面提到的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/380197618fcc8a3bbfd5149d990d281f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个哈希函数(置换)，我们事先取","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/38/380197618fcc8a3bbfd5149d990d281f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"个独立的随机种子值与之一一对应，每个随机种子就是哈希函数的替代。对于每个新闻及每个种子值，我们利用该种子值和该新闻的Id(是整数值)，利用一个特定的哈希函数","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"计算出一个哈希值，该哈希值作为利用前面讲的通过置换后该新闻的下标，那么采用这种方法后用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的哈希计算公式如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b4/b47522388ff3f85420baef58842e5d98.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"该方法不需要对新闻集进行置换，会大大减少计算量，并且只要这个特定哈希函数","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c6/c6bb184a9ca6777b008ecb594f385adb.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的取值范围在0到","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/24/2421b1f2e7bbd9d01aa35cd3998a08c6.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"之间，那么冲突概率就会比较小，通过这种近似的MinHash值与真正的MinHash值性质近似。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面讲解了MinHash聚类的算法实现细节，具体工程实现时是可以用Hadoop或者Spark等分布式计算平台来并行计算的，这里不细说。我们可以将每个用户的聚类及每个聚类包含的用户用倒排索引表的格式存储起来，方便后面做推荐时查阅。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"7.6.2 基于聚类为用户做推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了用户的聚类，我们可以采用如下步骤来为单个用户生成个性化推荐，每个用户的推荐策略是一样的，所以可以采用分布式计算平台Spark等工具来并行化处理。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(1) 计算出用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(2) 计算出用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对所有新闻的评分","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"(3) 将所有新闻评分降序排列，取topK作为该用户的推荐","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的(2)、(3)是非常简单的处理，我们重点来说一下(1)，怎么计算用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分。首先我们可以得到用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所属的所有类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/63/63cd7f3081339785220e1858f3cfd670.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，对于每个类别","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a37920d3e6468af62c1a9de73f258ea.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"，取出该类别中所有的用户对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的点击次数之和(我们可以事先将每个类别中用户点击过的新闻及次数存储起来，方便查找)，再除以该类别所有点击之和，得到该类别对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分，那么用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所属的类别对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的总评分为：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9e/9e757ebf2053de8d667ded3ae9b61f30.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/be/be367d506b1ddaed3b24c5f833c7c66d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"即是刚刚提到的类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6f8d94c92537d44931e7c475aa400fa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中所有用户对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"点击次数之和，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/c3/c347ed887b6aa2c83534e3cde1b3de49.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是类","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b6/b6f8d94c92537d44931e7c475aa400fa.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所有用户的所有点击次数之和。我们用上式计算出的","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5f/5f9d6288735b7de534116ba9243f5cd5.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"来表示用户","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/55/55f53a249a23d52ca0fb54de99a6a96d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"对新闻","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/85/85d7ed0729c0a85d691aad61038d8f7d.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的评分。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"至此，基于作者自己的理解，简单介绍完了Google News基于用户聚类的推荐算法。该方法也只用到了用户及其他用户的新闻点击行为，因此也是一种协同过滤算法，该算法的细节读者可以阅读参考文献3。参考文献17、18、19、20有更多关于怎么用聚类来做推荐的算法，感兴趣的读者可以参考学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"总结","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本章讲解了关联规则、朴素贝叶斯、聚类等三类基础机器学习算法怎么用于个性化推荐的理论知识，同时从算法原理和工程实现的角度简单总结了YouTube和Google News的三篇分别采用关联规则、朴素贝叶斯、聚类思路来做推荐的论文。这几篇论文有很强的工程指导意义，值得读者学习。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"虽然这些算法原理简单、容易理解，看起来不那么高大上，但是这些算法却在工业界有过非常好的应用，在当时算是非常优秀的算法。这些算法现在可能看起来太简单了，也可能不会用在现在的推荐系统上，但它们朴素的思想下面蕴含的是深刻的道理，值得我们推荐从业者学习、思考、借鉴，希望读者可以很好地理解它们，并吸收这些朴素思想背后的精华。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"参考文献","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. The YouTube Video Recommendation System","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"2. Personalized News Recommendation Based on Click Behavior ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"3. Google news personalization: Scalable online collaborative flitering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"4. Robustness of collaborative recommendation based on association rule mining","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"5. Analysis of recommendation algorithms for e-commerce","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"6. Fast algorithms for mining association rules","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"7. Efficient adaptive-support association rule mining for recommender systems","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"8. Mining navigation history for recommendation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"9. Collaborative filtering by mining association rules from user acess sequences","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"10. Mining frequent patterns without candidate generation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"11. Pfp: parallel fp-growth for query recommendation","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"12. Mining sequential patterns by pattern-growth: the PrefixSpan approach","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"13. Empirical analysis of predictive algorithms for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"14. A Bayesian model for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"15. Collaborative filtering with the simple Bayesian classifier","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"16. Probabilistic memory-based collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"17. Clustering methods for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"18. Rectree: A efficient collaborative filtering method","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"19. Scalable collaborative filtering using cluster-based smoothing","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"20. Latent class models for collaborative filtering","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]}]}
發表評論
所有評論
還沒有人評論，想成為第一個評論的人麼? 請在上方評論欄輸入並且點擊發布.
相關文章
应用星探｜别笑，这三款应用真的超“机智”！
前言 歡迎大家來到最新一期的應用星探系列，今天，我們就來盤點那些在AI原生應用中嶄露頭角的創意王者。如果對AI原生應用感興趣的朋友後續可以持續關注哦～ Ai technology
AppBuilder低代码体验：构建雅思大作文组件
Ai technology 前言 AppBuilder上線了低代碼製作組件功能，可以通過工作流的方式構建自定義組件，完成簡單Agent無法完成的複雜功能，使得生成的文本更加定製化，