Implementation of ALS

gistfile1.txt

def weighted_alternating():

  Q=[[5,3,0,1],[4,0,0,1],[1,1,0,5],[1,0,0,4],[0,1,5,4]]
	Q = np.array(Q)	

	# Create the weight matrix
	W = Q>0
	
	W[W == True] = 1
	W[W == False] = 0
	# To be consistent with our Q matrix
	W = W.astype(np.float64, copy=False)

	lambda_ = 0.1
	n_factors = 2
	m, n = Q.shape
	n_iterations = 20

	X = 5 * np.random.rand(m, n_factors) 
	Y = 5 * np.random.rand(n_factors, n)

	weighted_errors =[]

	start = time.time()
	for ii in range(n_iterations):
		
		for u,Wu in enumerate(W):
		
			X[u] = np.linalg.solve(np.dot(Y, np.dot(np.diag(Wu), Y.T)) + lambda_ * np.eye(n_factors),np.dot(Y, np.dot(np.diag(Wu), Q[u].T))).T

		for i, Wi in enumerate(W.T):
			
			 
			 Y[:,i] = np.linalg.solve(np.dot(X.T, np.dot(np.diag(Wi), X))+ lambda_ * np.eye(n_factors), np.dot(X.T, np.dot(np.diag(Wi), Q[:, i])))


		error = np.sum((W * (Q - np.dot(X, Y)))**2)
		print error
		weighted_errors.append(error)

	elapsed = (start-time.time())

	Q_hat = np.dot(X,Y)