Alternating Minimization in Tensorflow (PCA example)

pca_alt_min.py

import numpy as np
import tensorflow as tf

# N, size of matrix. R, rank of data
N = 100
R = 5

# generate data
W_true = np.random.randn(N,R)
C_true = np.random.randn(R,N)
Y_true = np.dot(W_true, C_true)
Y_tf = tf.constant(Y_true.astype(np.float32))

W = tf.Variable(np.random.randn(N,R).astype(np.float32), name='W')
C = tf.Variable(np.random.randn(R,N).astype(np.float32), name='C')
Y_est = tf.matmul(W,C)
loss = tf.reduce_sum((Y_tf-Y_est)**2)

# regularization 
alpha = tf.constant(1e-4)
regW = alpha*tf.reduce_sum(W**2)
regC = alpha*tf.reduce_sum(C**2)

# full objective
objective = loss + regW + regC

# optimization setup
optimizer = tf.train.AdamOptimizer(0.001)
train_step = optimizer.minimize(objective, var_list=[W,C])
train_W = optimizer.minimize(objective, var_list=[W])
train_C = optimizer.minimize(objective, var_list=[C])

# fit the model
init_op = tf.initialize_all_variables()
with tf.Session() as sess:
    sess.run(init_op)
    for n in range(10000):
        # update W
        sess.run(train_W)

        # update C
        _,objval = sess.run([train_C, objective])

        # print progress
        if (n+1) % 1000 == 0:
            print('iter %i, %f' % (n+1, objval))

It's just a auto-encoder..??

Is there any side effect that you train W, C separqately? Is it the same you put them together?