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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], | |
outputs=cost, | |
updates=[(P, P - gp * alpha), (Q, Q - gq * alpha)]) | |
for _ in xrange(steps): | |
train(D) | |
return P.get_value(), Q.get_value() | |
def matrix_factorization_sgd( | |
D, P, Q, steps=5000, alpha=0.0002, beta=0.02): | |
P = theano.shared(P.astype(floatX)) | |
Q = theano.shared(Q.astype(floatX)) | |
P_i = T.vector() | |
Q_j = T.vector() | |
i = T.iscalar() | |
j = T.iscalar() | |
x = T.scalar() | |
error = T.sqr(P_i.dot(Q_j) - x) | |
regularization = (beta/2.0) * (P_i.dot(P_i) + Q_j.dot(Q_j)) | |
cost = error + regularization | |
gp, gq = T.grad(cost=cost, wrt=[P_i, Q_j]) | |
train = theano.function(inputs=[i, j, x], | |
givens=[(P_i, P[i, :]), (Q_j, Q[:, j])], | |
updates=[(P, T.inc_subtensor(P[i, :], -gp * alpha)), | |
(Q, T.inc_subtensor(Q[:, j], -gq * alpha))]) | |
for _ in xrange(steps): | |
for (row, col), val in np.ndenumerate(D): | |
if not getmask(D)[row, col]: | |
train(row, col, val) | |
return P.get_value(), Q.get_value() | |
def matrix_factorization_quux( | |
D, P, Q, steps=5000, alpha=0.0002, beta=0.02): | |
K = P.shape[1] | |
P = np.copy(P) | |
Q = np.copy(Q) | |
for step in xrange(steps): | |
for i in xrange(len(D)): | |
for j in xrange(len(D[i])): | |
if not getmask(D)[i, j]: | |
eij = D[i, j] - np.dot(P[i, :], Q[:, j]) | |
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]) | |
return P, Q | |
if __name__ == '__main__': | |
D = np.array([[5, 3, -1, 1], | |
[4, -1, -1, 1], | |
[1, 1, -1, 5], | |
[1, -1, -1, 4], | |
[-1, 1, 5, 5]]) | |
D = ma.masked_array(D, mask=D==-1) | |
m, n = D.shape | |
K = 2 | |
P = np.random.rand(m, K) | |
Q = np.random.rand(K, n) | |
np.set_printoptions(formatter={'all': lambda x: str(x).rjust(2)}) | |
print 'Ratings Matrix\n', D, '\n' | |
np.set_printoptions(precision = 2, formatter=None) | |
P_theano_bgd, Q_theano_bgd = matrix_factorization_bgd(D, P, Q) | |
print 'Theano Batch Gradient Descent\n',\ | |
np.dot(P_theano_bgd, Q_theano_bgd), '\n' | |
P_theano_sgd, Q_theano_sgd = matrix_factorization_sgd(D, P, Q) | |
print 'Theano Stochastic Gradient Descent\n',\ | |
np.dot(P_theano_sgd, Q_theano_sgd), '\n' | |
P_quux, Q_quux = matrix_factorization_quux(D, P, Q) | |
print 'quuxlabs\n', np.dot(P_quux, Q_quux), '\n' |
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