LFM推薦的例子和代碼

參考自鄒博的博客！
LFM：將評分矩陣分解爲 item-feature 和 user-feature矩陣，feature數量事先人工確定，但是這兩個矩陣參數未知，首先隨機選取參數，再以此梯度下降迭代即可得到。

import pandas as pd
import numpy as np

def lfm(user_item,k,alpha = 0.01,lamda = 0.01):
    """user_item is matrix of user item,k is the number of latent number"""
    if not isinstance(user_item,list):
        raise("user item:{user_item} is not a matrix list!".format(user_item=user_item))
    mat = np.array(user_item)
    user_number,item_number = mat.shape
    # init the user and item latent matrix
    u = np.random.rand(user_number,k)
    v = np.random.rand(item_number,k)
    for it in range(1000):
        for i in range(user_number):
            for j in range(item_number):
                # err
                err = user_item[i][j] - np.dot(u[i],v[j])
                for r in range(k):
                    gu = err * v[j][r] + lamda * u[i][r]
                    gv = err * u[i][r] + lamda * v[j][r]
                    u[i][r] += alpha * gu
                    v[j][r] += alpha * gv
    return u,v
if __name__ == "__main__":
    mat = [[5,5,0,5],[5,0,3,4],[3,4,0,3],[0,0,5,3],[5,4,4,5],[5,4,5,5]]
    u,v = lfm(mat,3)
    print u
    print v
    print np.dot(u,v.T)

初始評分矩陣

[[5,5,0,5],[5,0,3,4],[3,4,0,3],[0,0,5,3],[5,4,4,5],[5,4,5,5]]

迭代後的u v 矩陣

[[ 0.18447051  2.09168616  0.8831042 ]
 [ 1.7912757   1.24549537 -0.48677593]
 [-0.1002325   1.29114151  0.86229546]
 [ 1.38787106 -0.70947744  0.76619629]
 [ 1.26487691  1.27983092  1.02112708]
 [ 1.48243041  1.08592233  1.13930052]]

[[ 1.30296976  2.33056037  0.22352664]
 [-0.38291845  1.51851172  2.39872099]
 [ 2.63593771 -0.74171661  1.47001405]
 [ 1.59681827  1.36696209  1.48520738]]

預測的結果

[[ 5.31255767  5.22393338  0.23298999  4.46541444]
 [ 5.12787282  0.03774717  3.08231911  3.83992351]
 [ 3.07122934  4.06740062  0.04571872  2.88557601]
 [ 0.3261393   0.22909989  5.31089216  2.38430948]
 [ 4.85906868  3.9084925   3.88593604  5.28584437]
 [ 4.71703356  3.81419992  4.77693537  5.54368417]]

結果接近，效果還行。
如果來一個未對item1評分的user1，但是user1和item1的feature我們知道即上面的u1和v1，只需要u1 * v1.T即可得到5.31. 這樣就可以有針對性的進行推薦了。