矩阵分解法做推荐系统

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# !/usr/bin/env python
# encoding: utf-8
__author__ = 'Scarlett'
#矩阵分解在打分预估系统中得到了成熟的发展和应用
# from pylab import *
import matplotlib.pyplot as plt
from math import pow
import numpy


def matrix_factorization(R,P,Q,K,steps=5000,alpha=0.0002,beta=0.02):
    Q=Q.T  # .T操作表示矩阵的转置
    result=[]
    for step in range(steps):
        for i in range(R.shape[0]):
            for j in range(R.shape[1]):
                if R[i][j]>0:
                    eij=R[i][j]-numpy.dot(P[i,:],Q[:,j]) # .dot(P,Q) 表示矩阵内积
                    for k in range(K):
                        P[i][k]=P[i][k]+alpha*(2*eij*Q[k][j]-beta*P[i][k])
                        Q[k][j]=Q[k][j]+alpha*(2*eij*P[i][k]-beta*Q[k][j])
#        eR=numpy.dot(P,Q)
#        e=0
#        for i in range(R.shape[0]):
#            for j in range(R.shape[1]):
#                if R[i][j]>0:
#                    e=e+pow(R[i][j]-numpy.dot(P[i,:],Q[:,j]),2)
#                    for k in range(K):
#                        e=e+(beta/2)*(pow(P[i][k],2)+pow(Q[k][j],2))
#        result.append(e)
#        if e<0.001:
#            break
    return P,Q.T,result

if __name__ == '__main__':

    
    R= [[4., 3., 0., 5., 0.],
        [5., 0., 4., 4., 0.],
        [4., 0., 5., 0., 3.],
        [2., 3., 0., 1., 0.],
        [0., 4., 2., 0., 5.]]

    R=numpy.array(R)

    M=R.shape[0]
    N=R.shape[1]
    K=2

    P=numpy.random.rand(N,K) #随机生成一个 N行 K列的矩阵
    Q=numpy.random.rand(M,K) #随机生成一个 M行 K列的矩阵

    nP,nQ,result=matrix_factorization(R,P,Q,K)
    print("原始的评分矩阵R为：\n",R)
    R_MF=numpy.dot(nP,nQ.T)
    print("经过MF算法填充0处评分值后的评分矩阵R_MF为：\n",R_MF)

##-------------损失函数的收敛曲线图---------------
#
#    n=len(result)
#    x=range(n)
#    plt.plot(x,result,color='r',linewidth=3)
#    plt.title("Convergence curve")
#    plt.xlabel("generation")
#    plt.ylabel("loss")
#    plt.show()