自编码Autoencoder（非监督学习）

Autoencoder

# Parameter
learning_rate=0.01
training_epochs=5
# 五组训练
batch_size=256
display_step=1
examples_to_show=10

MNIST数据，每张图片大小是 28x28 pix，即 784 Features：

# Network Parameters
n_input=784
# MNIST data input (img shape: 28*28)

# hidden layer settings
n_hidden_1 = 256 # 1st layer num features
n_hidden_2 = 128 # 2nd layer num features
weights = {
    'encoder_h1':tf.Variable(tf.random_normal([n_input,n_hidden_1])),
    'encoder_h2': tf.Variable(tf.random_normal([n_hidden_1,n_hidden_2])),
    'decoder_h1': tf.Variable(tf.random_normal([n_hidden_2,n_hidden_1])),
    'decoder_h2': tf.Variable(tf.random_normal([n_hidden_1, n_input])),
    }
biases = {
    'encoder_b1': tf.Variable(tf.random_normal([n_hidden_1])),
    'encoder_b2': tf.Variable(tf.random_normal([n_hidden_2])),
    'decoder_b1': tf.Variable(tf.random_normal([n_hidden_1])),
    'decoder_b2': tf.Variable(tf.random_normal([n_input])),
    }

压缩之后的值在 [0,1] 这个范围内。在decoder过程中，通常使用对应于encoder的 Activation function：

# Building the encoder
def encoder(x):
    # Encoder Hidden layer with sigmoid activation #1
    layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['encoder_h1']),
                                   biases['encoder_b1']))
    # Decoder Hidden layer with sigmoid activation #2
    layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['encoder_h2']),
                                   biases['encoder_b2']))
    return layer_2

# Building the decoder
def decoder(x):
    # Encoder Hidden layer with sigmoid activation #1
    layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['decoder_h1']),
                                   biases['decoder_b1']))
    # Decoder Hidden layer with sigmoid activation #2
    layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['decoder_h2']),
                                   biases['decoder_b2']))
    return layer_2

# Construct model
encoder_op = encoder(X)             # 128 Features
decoder_op = decoder(encoder_op)    # 784 Features

# Prediction
y_pred = decoder_op    # After 
# Targets (Labels) are the input data.
y_true = X            # Before

对 “原始的有 784 Features 的数据集” 和 “通过 ‘Prediction’ 得出的有 784 Features 的数据集” 进行最小二乘法的计算，并且使 cost 最小化:

# Define loss and optimizer, minimize the squared error
cost = tf.reduce_mean(tf.pow(y_true - y_pred, 2))
optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost)

输出时MNIST数据集经过压缩之后 x 的最大值是1，而非255：

# Launch the graph
with tf.Session() as sess:
    # tf 马上就要废弃tf.initialize_all_variables()这种写法
    # 替换成下面:
    sess.run(tf.global_variables_initializer())
    total_batch = int(mnist.train.num_examples/batch_size)
    # Training cycle
    for epoch in range(training_epochs):
        # Loop over all batches
        for i in range(total_batch):
            batch_xs, batch_ys = mnist.train.next_batch(batch_size)  # max(x) = 1, min(x) = 0
            # Run optimization op (backprop) and cost op (to get loss value)
            _, c = sess.run([optimizer, cost], feed_dict={X: batch_xs})
        # Display logs per epoch step
        if epoch % display_step == 0:
            print("Epoch:", '%04d' % (epoch+1),
                  "cost=", "{:.9f}".format(c))

    print("Optimization Finished!")

    # # Applying encode and decode over test set
    encode_decode = sess.run(
        y_pred, feed_dict={X: mnist.test.images[:examples_to_show]})
    # Compare original images with their reconstructions
    f, a = plt.subplots(2, 10, figsize=(10, 2))
    for i in range(examples_to_show):
        a[0][i].imshow(np.reshape(mnist.test.images[i], (28, 28)))
        a[1][i].imshow(np.reshape(encode_decode[i], (28, 28)))
    plt.show()

Encoder

# Parameters
learning_rate = 0.01    # 0.01 this learning rate will be better! Tested
training_epochs = 10    # 10 Epoch 训练
batch_size = 256
display_step = 1

通过四层 Hidden Layers 实现将 784 Features 压缩至 2 Features：

# hidden layer settings
n_hidden_1 = 128
n_hidden_2 = 64
n_hidden_3 = 10
n_hidden_4 = 2

weights = {
    'encoder_h1': tf.Variable(tf.truncated_normal([n_input, n_hidden_1],)),
    'encoder_h2': tf.Variable(tf.truncated_normal([n_hidden_1, n_hidden_2],)),
    'encoder_h3': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_3],)),
    'encoder_h4': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_4],)),

    'decoder_h1': tf.Variable(tf.truncated_normal([n_hidden_4, n_hidden_3],)),
    'decoder_h2': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_2],)),
    'decoder_h3': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_1],)),
    'decoder_h4': tf.Variable(tf.truncated_normal([n_hidden_1, n_input],)),
    }
biases = {
    'encoder_b1': tf.Variable(tf.random_normal([n_hidden_1])),
    'encoder_b2': tf.Variable(tf.random_normal([n_hidden_2])),
    'encoder_b3': tf.Variable(tf.random_normal([n_hidden_3])),
    'encoder_b4': tf.Variable(tf.random_normal([n_hidden_4])),

    'decoder_b1': tf.Variable(tf.random_normal([n_hidden_3])),
    'decoder_b2': tf.Variable(tf.random_normal([n_hidden_2])),
    'decoder_b3': tf.Variable(tf.random_normal([n_hidden_1])),
    'decoder_b4': tf.Variable(tf.random_normal([n_input])),
    }

在第四层时，输出量不再是 [0,1] 范围内的数，而是将数据通过默认的 Linear activation function 调整为 (-∞,∞) ：

def encoder(x):
    layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['encoder_h1']),
                                   biases['encoder_b1']))
    layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['encoder_h2']),
                                   biases['encoder_b2']))
    layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights['encoder_h3']),
                                   biases['encoder_b3']))
    layer_4 = tf.add(tf.matmul(layer_3, weights['encoder_h4']),
                                    biases['encoder_b4'])
    return layer_4


def decoder(x):
    layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights['decoder_h1']),
                                   biases['decoder_b1']))
    layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights['decoder_h2']),
                                   biases['decoder_b2']))
    layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights['decoder_h3']),
                                biases['decoder_b3']))
    layer_4 = tf.nn.sigmoid(tf.add(tf.matmul(layer_3, weights['decoder_h4']),
                                biases['decoder_b4']))
    return layer_4

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np

tf.set_random_seed(1)

# Hyper Parameters
BATCH_SIZE = 64
LR = 0.002         # learning rate
N_TEST_IMG = 5

# Mnist digits
mnist = input_data.read_data_sets('./mnist', one_hot=False)     # use not one-hotted target data
test_x = mnist.test.images[:200]
test_y = mnist.test.labels[:200]

# plot one example
print(mnist.train.images.shape)     # (55000, 28 * 28)
print(mnist.train.labels.shape)     # (55000, 10)
plt.imshow(mnist.train.images[0].reshape((28, 28)), cmap='gray')
plt.title('%i' % np.argmax(mnist.train.labels[0]))
plt.show()

# tf placeholder
tf_x = tf.placeholder(tf.float32, [None, 28*28])    # value in the range of (0, 1)

# encoder
en0 = tf.layers.dense(tf_x, 128, tf.nn.tanh)
en1 = tf.layers.dense(en0, 64, tf.nn.tanh)
en2 = tf.layers.dense(en1, 12, tf.nn.tanh)
encoded = tf.layers.dense(en2, 3)

# decoder
de0 = tf.layers.dense(encoded, 12, tf.nn.tanh)
de1 = tf.layers.dense(de0, 64, tf.nn.tanh)
de2 = tf.layers.dense(de1, 128, tf.nn.tanh)
decoded = tf.layers.dense(de2, 28*28, tf.nn.sigmoid)

loss = tf.losses.mean_squared_error(labels=tf_x, predictions=decoded)
train = tf.train.AdamOptimizer(LR).minimize(loss)

sess = tf.Session()
sess.run(tf.global_variables_initializer())

# initialize figure
f, a = plt.subplots(2, N_TEST_IMG, figsize=(5, 2))
plt.ion()   # continuously plot

# original data (first row) for viewing
view_data = mnist.test.images[:N_TEST_IMG]
for i in range(N_TEST_IMG):
    a[0][i].imshow(np.reshape(view_data[i], (28, 28)), cmap='gray')
    a[0][i].set_xticks(()); a[0][i].set_yticks(())

for step in range(8000):
    b_x, b_y = mnist.train.next_batch(BATCH_SIZE)
    _, encoded_, decoded_, loss_ = sess.run([train, encoded, decoded, loss], {tf_x: b_x})

    if step % 100 == 0:     # plotting
        print('train loss: %.4f' % loss_)
        # plotting decoded image (second row)
        decoded_data = sess.run(decoded, {tf_x: view_data})
        for i in range(N_TEST_IMG):
            a[1][i].clear()
            a[1][i].imshow(np.reshape(decoded_data[i], (28, 28)), cmap='gray')
            a[1][i].set_xticks(()); a[1][i].set_yticks(())
        plt.draw(); plt.pause(0.01)
plt.ioff()

# visualize in 3D plot
view_data = test_x[:200]
encoded_data = sess.run(encoded, {tf_x: view_data})
fig = plt.figure(2); ax = Axes3D(fig)
X, Y, Z = encoded_data[:, 0], encoded_data[:, 1], encoded_data[:, 2]
for x, y, z, s in zip(X, Y, Z, test_y):
    c = cm.rainbow(int(255*s/9)); ax.text(x, y, z, s, backgroundcolor=c)
ax.set_xlim(X.min(), X.max()); ax.set_ylim(Y.min(), Y.max()); ax.set_zlim(Z.min(), Z.max())
plt.show()