Implementation of Weighted Matrix Factorization for Implicit Feedbacks

wmf.py

import numpy
from numpy import random
from numpy import linalg

def WMF(R,k=10,alpha=0.1,beta=10.,max_iteration=100000,stop_criterion=1e-6):
    """
    R: feedback matrix like R_ij represents the number that user_i clicks item_j
    k: dimensionality of latent factor vector
    alpha: regularization parameter
    beta: confidence parameter
    max_iteration: max number of iteration
    stop_criterion: the number representing stop criterion
    """
    m,n=R.shape
    P=(R>0)*1. # preference matrix
    C=1.+beta*R # confidence matrix
    X=random.rand(m,k)
    Y=random.rand(n,k)
    for itr in xrange(max_iteration):
        Xold=X.copy()
        Yold=Y.copy()
        for i in xrange(m):
            ri=P[i]
            ci=C[i]
            if sum(ci)==0:
                continue
            X[i]=numpy.dot(linalg.pinv(numpy.dot(Y.T,numpy.c_[ci]*Y)+alpha*numpy.identity(k)),numpy.dot(Y.T,ci*ri))
        for j in xrange(n):
            rj=P[:,j]
            cj=C[:,j]
            if sum(cj)==0:
                continue
            Y[j]=numpy.dot(linalg.pinv(numpy.dot(X.T,numpy.c_[cj]*X)+alpha*numpy.identity(k)),numpy.dot(X.T,cj*rj))
        if linalg.norm(X-Xold)+linalg.norm(Y-Yold)<stop_criterion:
            break
    return X,Y

Note: It takes a long time...