implicit_feedback_als_3.py

""" Continuation of implicit_als function"""

    # Start main loop. For each iteration we first compute X and then Y
    for i in xrange(iterations):
        print 'iteration %d of %d' % (i+1, iterations)
        
        # Precompute Y-transpose-Y and X-transpose-X
        yTy = Y.T.dot(Y)
        xTx = X.T.dot(X)

        # Loop through all users
        for u in xrange(user_size):

            # Get the user row.
            u_row = confidence[u,:].toarray() 

            # Calculate the binary preference p(u)
            p_u = u_row.copy()
            p_u[p_u != 0] = 1.0

            # Calculate Cu and Cu - I
            CuI = sparse.diags(u_row, [0])
            Cu = CuI + Y_I

            # Put it all together and compute the final formula
            yT_CuI_y = Y.T.dot(CuI).dot(Y)
            yT_Cu_pu = Y.T.dot(Cu).dot(p_u.T)
            X[u] = spsolve(yTy + yT_CuI_y + lI, yT_Cu_pu)

    
        for i in xrange(item_size):

            # Get the item column and transpose it.
            i_row = confidence[:,i].T.toarray()

            # Calculate the binary preference p(i)
            p_i = i_row.copy()
            p_i[p_i != 0] = 1.0

            # Calculate Ci and Ci - I
            CiI = sparse.diags(i_row, [0])
            Ci = CiI + X_I

            # Put it all together and compute the final formula
            xT_CiI_x = X.T.dot(CiI).dot(X)
            xT_Ci_pi = X.T.dot(Ci).dot(p_i.T)
            Y[i] = spsolve(xTx + xT_CiI_x + lI, xT_Ci_pi)

    return X, Y