I used and modified a matrix factorization function for a system recommender from quuxlabs.com. It works well for small sized input but when we get to large matrix it takes too much time. I was wondering if you had any idea to code it better to optimize the time it would take.
Here R is the rating matrix of a user with an item. 0 means that nothing has been predicted yet, the one we have to predict. K is the number of extrab features. P and Q are scores matrix on latent features that would help predict R as a whole.
import numpy def matrix_factorization(R, P, Q, K, steps=5000, alpha=0.0002, beta=0.02): Q = Q.T for step in xrange(steps): for i in xrange(len(R)): for j in xrange(len(R[i])): if R[i][j] > 0: try: eij = R[i][j] - numpy.dot(P[i,:],Q[:,j]) except IndexError: print("Oops! i = ",i,"and len(P) = ",len(P)) P[i,:] break for k in xrange(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 xrange(len(R)): for j in xrange(len(R[i])): if R[i][j] > 0: e = e + pow(R[i][j] - numpy.dot(P[i,:],Q[:,j]), 2) for k in xrange(K): e = e + (beta/2) * (pow(P[i][k],2) + pow(Q[k][j],2)) if e < 0.001: break return P, Q.T
It works well with the following input :
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) K = 2 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)
Yet, on real big matrix, the function took so long that I eventually cancelled it because I got tired of waiting.