矩陣分解推薦算法(十八)

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"寫在前面：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"大家好，我是強哥，一個熱愛分享的技術狂。目前已有 12 年大數據與AI相關項目經驗， 10 年推薦系統研究及實踐經驗。平時喜歡讀書、暴走和寫作。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"業餘時間專注於輸出大數據、AI等相關文章，目前已經輸出了40萬字的推薦系統系列精品文章，今年 6 月底會出版「構建企業級推薦系統：算法、工程實現與案例分析」一書。如果這些文章能夠幫助你快速入門，實現職場升職加薪，我將不勝歡喜。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"想要獲得更多免費學習資料或內推信息，一定要看到文章最後喔。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"內推信息","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你正在看相關的招聘信息，請加我微信：liuq4360，我這裏有很多內推資源等着你，歡迎投遞簡歷。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"免費學習資料","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想獲得更多免費的學習資料，請關注同名公衆號【數據與智能】，輸入“資料”即可！","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"學習交流羣","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果你想找到組織，和大家一起學習成長，交流經驗，也可以加入我們的學習成長羣。羣裏有老司機帶你飛，另有小哥哥、小姐姐等你來勾搭！加小姐姐微信：epsila，她會帶你入羣。","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":"作者在《協同過濾推薦算法》中介紹了user-based和item-based協同過濾算法，這類協同過濾算法是基於鄰域的算法(也稱爲基於內存的協同過濾算法)，該算法不需要模型訓練，基於非常樸素的“物以類聚”、“人以羣分”的思想就可以爲用戶生成推薦結果。還有一類基於隱因子(模型)的協同過濾算法也非常重要，這類算法中最重要的代表就是本章我們要講的矩陣分解算法。矩陣分解算法是2006年Netflix推薦大賽獲獎的核心算法，在整個推薦系統發展史上具有舉足輕重的地位，對促進推薦系統的大規模發展及工業應用功不可沒。","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":"本章我們會詳細介紹矩陣分解算法的方方面面。我們會從矩陣分解算法的核心思想、矩陣分解的算法原理、矩陣分解算法的求解方法、矩陣分解算法的拓展與優化、近實時矩陣分解算法、矩陣分解算法的應用場景、矩陣分解算法的優缺點等7個方面來講解矩陣分解算法。希望通過本章的學習，讀者可以很好地瞭解矩陣分解的算法原理與工程實現，並且具備自己動手實踐矩陣分解算法的能力，可以嘗試將矩陣分解算法應用到推薦業務中。","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":"8.1 矩陣分解推薦算法的核心思想","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我們在《協同過濾推薦算法》這一章中講過，用戶操作行爲可以轉化爲如下的用戶行爲矩陣。其中","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/13/1312e517bedf6d1405acbb2feb9c5383.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"是用戶i 對標的物 j 的評分，如果是隱式反饋，值爲0或者1(隱式反饋可以通過一定的策略轉化爲得分，具體參考《協同過濾推薦算法》這一章中的介紹)，本文我們主要用顯示反饋(用戶的真實評分)來講解矩陣分解算法，對於隱式反饋，我們會在8.4.5中專門講解和說明。","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/39/39412800c70010ff6bd83f9f772e08dd.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"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":"圖1：用戶對標的物的操作行爲矩陣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/11/1148257bfcad58080e27656dd43acc80.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"矩陣分解算法是將用戶評分矩陣","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":"分解爲兩個矩陣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3f/3fbd292b5cac64fc8bd79ce194f5d66a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","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/8b/8b798e3723ba8003d05c551e21f79596.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的乘積。","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/55/5580842bb96c8e60046d4767f58d7f7e.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","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/3f/3fbd292b5cac64fc8bd79ce194f5d66a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"代表的用戶特徵矩陣，","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8b/8b798e3723ba8003d05c551e21f79596.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"代表標的物特徵矩陣。","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":"某個用戶對某個標的物的評分，就可以採用矩陣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/3f/3fbd292b5cac64fc8bd79ce194f5d66a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"對應的行(該用戶的特徵向量)與矩陣","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/8b/8b798e3723ba8003d05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應用於標的物關聯標的物場景(標的物關聯標的物範式)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"標的物關聯標的物推薦就是爲每個標的物關聯一組相似/相關的標的物作爲推薦。前面我們沒有直接講到怎麼做標的物關聯推薦。但是，如果我們得到了每個標的物的特徵向量(通過矩陣分解，獲得的標的物嵌入k維特徵空間的向量)，那麼我們可以通過向量的cosine餘弦相似度來獲得與某個標的物最相似的K個標的物作爲關聯推薦結果。有了標的物特徵向量後具體怎麼工程實現，計算topK相似度，讀者可以參考第5章《協同過濾推薦算法》6.3.1節中計算topK相似度的方法來實現，原理是完全一樣的，這裏不再贅述。","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":"下圖是電視貓視頻的相似推薦，它就是一種關聯推薦，關聯推薦大量用於電商、視頻、新聞等產品中。","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/68/6832852f6326b0a1e78d48d43fae6e07.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"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":"圖7：電視貓詳情頁相似影片：視頻關聯視頻的推薦，可以基於標的物特徵向量來計算關聯推薦","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":"8.6.3 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應用於羣組個性化場景(羣組個性化推薦範式)","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在8.6.3中我們講了用戶聚類，當用戶聚類後，我們可以對同一類用戶提供相同的推薦服務，這時就是羣組個性化推薦。羣組個性化推薦相當於將有相同興趣偏好的個體看成一個等價類，統一爲他們提供推薦，它是介於完全個性化推薦(每個人推薦的都不一樣)和完全非個性化推薦(所有人推薦的都一樣)之間的一種推薦形態。","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":"我們對電視貓的站點樹內容做的個性化重排序就是採用的基於矩陣分解獲取用戶特徵向量再對用戶聚類的技術。首先對用戶聚類，同一類的用戶通過特徵向量平均獲得該類的中心特徵向量，該中心特徵向量代表了該羣組的特徵，我們再用該向量跟標的物特徵向量求cosine餘弦，最終獲得該中心向量跟所有標的物特徵向量的相似度。在站點樹重排中，對站點樹的所有節目，可以獲得中心向量與站點樹節目特徵向量的相似度，按照該相似度降序排列就獲得了該羣組的重排序結果。下圖就是電視貓電視劇頻道“","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"戰爭風雲","attrs":{}},{"type":"text","text":"”站點樹重排序的產品形態(每個用戶看到的戰爭風雲總節目量是一樣的，只是排序不一樣，會按照用戶的興趣[其實是用戶所在羣組的平均興趣]將喜歡的排在前面)。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4d/4d358b6217a78447e0db59d232555dba.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"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":"圖8：電視貓站點樹個性化排序：基於羣組個性化爲用戶做推薦","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":"除了上面的應用場景外，由矩陣分解獲得的用戶和標的物特徵向量，可以作爲其他模型(如深度學習模型)的特徵輸入，進一步訓練更復雜的模型。","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":"8.7 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不依賴用戶和標的物的其他信息，只需要用戶行爲就可以爲用戶做推薦","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"矩陣分解算法也是一類協同過濾算法，它只需要用戶行爲就可以爲用戶生成推薦結果，而不需要用戶或者標的物的其他信息，而這類其他信息往往是半結構化或者非結構化的信息，不易處理，有時也較難獲得。","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":"矩陣分解是領域無關的一類算法，因此，該優點可以讓矩陣分解算法基本可以應用於所有推薦場景中，這也是矩陣分解算法在工業界大受歡迎的重要原因。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 推薦精準度不錯","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"矩陣分解算法是Netflix推薦大賽中獲獎算法中非常重要的一類算法，準確度是得到業界一致認可和驗證的，作者所在公司的推薦業務中也大量利用矩陣分解算法，效果也是非常不錯的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(3) 可以爲用戶推薦驚喜的標的物","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"協同過濾算法利用羣體的智慧來爲用戶推薦，具備爲用戶推薦差異化、有驚喜度的標的物的能力，矩陣分解算法作爲協同過濾算法中一類基於隱因子的算法，當然也具備這個優點，甚至比user-based和item-based協同過濾算法有更好的效果。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(4) 易於並行化處理","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通過第三節矩陣分解的ALS求解過程，我們可以知道矩陣分解是非常容易並行化的，Spark MLlib庫中就是採用ALS算法進行分佈式矩陣分解的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"8.7.2 缺點","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面講了這麼多矩陣分解算法的優點，除了這些優點外，矩陣分解在下面這兩點上是有缺陷的，需要採用其他的算法和策略來彌補或者避免。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(1) 存在冷啓動問題","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"當某個用戶的操作行爲很少時，我們基本無法利用矩陣分解獲得該用戶比較精確的特徵向量表示，因此無法爲該用戶生成推薦結果。這時可以藉助內容推薦算法來爲該用戶生成推薦。","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":"對於新入庫的標的物也一樣，可以採用人工編排的方式將標的物做適當的曝光獲得更多用戶對標的物的操作行爲，從而方便算法將該標的物推薦出去。","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":"參考文獻9中提供了一種解決矩陣分解冷啓動問題的有效算法lightFM，通過將metadata信息整合到矩陣分解中，可以有效解決冷啓動問題，對於操作行爲不多的用戶以及新上線不久還未收集到足夠多用戶行爲的標的物都有比較好的推薦效果。該論文的lightFM算法在github上有相應的python代碼實現(參見","attrs":{}},{"type":"link","attrs":{"href":"https://github.com/lyst/lightfm","title":null,"type":null},"content":[{"type":"text","marks":[{"type":"underline","attrs":{}}],"text":"https://github.com/lyst/lightfm","attrs":{}}]},{"type":"text","text":")，可以作爲很好的學習材料。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"(2) 可解釋性不強","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"矩陣分解算法通過矩陣分解獲得用戶和標的物的(嵌入)特徵表示，這些特徵是隱式的，無法用現實中的顯示特徵進行解釋，因此利用矩陣分解算法做出的推薦，我們無法對推薦結果進行解釋，只能通過離線或者在線評估來評價算法的效果。不像user-based和item-based協同過濾算法基於非常樸素的”物以類聚、人以羣分“的思想，可以非常容易地進行解釋。但也不是絕對的，其中參考文獻5中的實現方法就提供了一個爲矩陣分解做推薦解釋的非常有建設性的思路。","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":"總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本文對矩陣分解算法原理、工程實踐、應用場景、優缺點等進行了比較全面的總結。矩陣分解算法是真正意義上的基於模型的協同過濾算法。通過將用戶和標的物嵌入到低維隱式特徵空間，獲得用戶和標的物的特徵向量表示，再通過向量的內積來量化用戶對標的物的興趣偏好，思路非常簡單、清晰，也易於工程實現，效果也相當不錯，所以在工業界有非常廣泛的應用。矩陣分解算法算是開啓了嵌入類方法的先河，在NLP領域非常出名的Word2Vec也是嵌入方法的代表，深度學習興起後，各類嵌入方法在大量的業務場景中得到了大規模的採用。","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":"參考文獻","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1. Real-time Video Recommendation Exploration","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"2. Real-Time Top-N Recommendation in Social Streams","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"3. Online-updating  regularized kernel matrix factorization models for large-scale recommender systems","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"4. Factorization Meets the Item Embedding- Regularizing Matrix Factorization with Item Co-occurrence","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"5. Collaborative Filtering for Implicit Feedback 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