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#ML之RS之MF：基于简单的张量分解MF算法进行打分和推荐import numpy def matrix_factorization(R, P, Q, K, steps=5000, alpha=0.0002, beta=0.02):  #（迭代次数5000、步长，正则化系数）    Q = Q.T    for step in range(steps):        for i in range(len(R)):            for j in range(len(R[i])):                if R[i][j] > 0:                    eij = R[i][j] - numpy.dot(P[i,:],Q[:,j])                    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(len(R)):            for j in range(len(R[i])):                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))        if e < 0.001:            break    return P, Q.T #读取user数据并用张量分解进行打分#定义得分矩阵R = [     [5,3,0,1],     [4,0,3,1],     [1,1,0,5],     [1,0,0,4],     [0,1,5,4],    ] R = numpy.array(R) N = len(R)M = len(R[0])K = 2  #两个因子 P = numpy.random.rand(N,K)Q = numpy.random.rand(M,K) nP, nQ = matrix_factorization(R, P, Q, K)nR = numpy.dot(nP, nQ.T) print(nP)print("-----------------------------")print(nQ)print("-----------------------------")print(nR)print("-----------------------------")print(R)

结果输出： 

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