nmf-ly.py

import numpy
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
   
def matrix_factorisation(R, P, Q, K, steps=5000, alpha=0.0002, beta=0.02):  
    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

R = [  
     [5,3,0,1],  
     [4,0,0,1],  
     [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  
   
P = numpy.random.rand(N,K)  
Q = numpy.random.rand(M,K)  
   
nP, nQ = matrix_factorisation(R, P, Q, K)  
nR = numpy.dot(nP, nQ.T)
print(nP)
# print(nQ)
print(Q.T)
print(nR)