matrix_factorization_bgd.py

import numpy as np
import numpy.ma as ma
import theano
from theano import tensor as T

floatX = theano.config.floatX


def getmask(D):
  return ma.getmaskarray(D) if ma.isMA(D) else np.zeros(D.shape, dtype=bool)


def matrix_factorization_bgd(
    D, P, Q, steps=5000, alpha=0.0002, beta=0.02):
  P = theano.shared(P.astype(floatX))
  Q = theano.shared(Q.astype(floatX))
  X = T.matrix()
  error = T.sum(T.sqr(~getmask(D) * (P.dot(Q) - X)))
  regularization = (beta/2.0) * (T.sum(T.sqr(P)) + T.sum(T.sqr(Q)))
  cost = error + regularization
  gp, gq = T.grad(cost=cost, wrt=[P, Q])
  train = theano.function(inputs=[X],
                          updates=[(P, P - gp * alpha), (Q, Q - gq * alpha)])
  for _ in xrange(steps):
    train(D)
  return P.get_value(), Q.get_value()