MF.py

import numpy as np
#迭代退出既控制次数又控制条件如果在迭代过程中能够提前退出就提前退出
def MF(R,P,Q,K,steps,alpha,beta):
    m, n = R.shape
    for step in range(steps):
        for i in range(m):
            for j in range(n):
                if R[i][j]:
                    eij = R[i][j] - np.dot(P[i,:],Q[:,j])#内积运算
                    for k in range(K):
                        P[i][k] += alpha * (2 * eij * Q[k][j] - beta * P[i][k])
                        Q[k][j] += alpha * (2 * eij * P[i][k] - beta * Q[k][j])
        #所有的变量更新一遍之后判断一下损失函数是否满足退出条件
        loss = 0
        for i in range(m):
            for j in range(n):
                if R[i][j]:
                    eij = R[i][j] - np.dot(P[i, :], Q[:, j])
                    loss += pow(eij,2)
                    for k in range(K):
                        loss += (beta / 2) * (pow(P[i][k],2)+pow(Q[k,j],2))
        if loss < 1.1 :
            return P,Q
if __name__ == '__main__':
    R = np.array([ [5, 3, 0, 1],
                   [4, 0, 0, 1],
                   [1, 0, 0, 4],
                   [0, 1, 5, 4],
                   [0, 1, 5, 4]])
    k = 5
    m, n = R.shape
    P = np.random.rand(m,k)#初始化 随便赋值就ok
    Q = np.random.rand(k,n)
    new_P,new_Q = MF(R,P,Q,k,2000000,0.0002,0.02)
    new_R = np.matmul(new_P,new_Q)
    print(new_P)
    print(new_Q)
    print(R)
    print(new_R)