学习笔记：自编码和稀疏自编码（TensorFlow代码）

本文链接：https://blog.youkuaiyun.com/m0_37744293/article/details/70767843

本文介绍稀疏自编码的基本概念及其实现方法，通过使用TensorFlow框架完成了一个针对MNIST数据集的稀疏自编码器模型，并展示了如何通过调整超参数优化模型效果。

一、稀疏自编码

假设我们只有一个没有类别标签的训练样本集合{x(1),x(2)…},一个自编码神经网络就是一种非监督学习算法，它使用BP算法，并将目标值设为输入值(y(i)=x(i))。

这里写图片描述

希望得到hW,b(X)≈x。用aj(2)(x)表示输入向量x对隐藏层单元j的激活值。则j的平均激活值：
这里写图片描述
为了达到稀疏性，也即用最少（最稀疏）的隐藏单元来表示输入层的特征，我们希望所有隐藏层单元平均激活值接近于0.于是应用KL距离：

另一种写法：

其中，代价函数为：

二，稀疏自编码的TensorFlow代码

自编码的原理在上一遍文章中已经讲解，详细请戳SAE

from __future__ import division, print_function, absolute_import

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

# 下载并导入MNIST数据集
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data", one_hot=True)

# 参数
learning_rate = 0.01#学习率
training_epochs = 20#训练的周期
batch_size = 256#每一批次训练的大小
display_step = 1
examples_to_show = 10

# 神经网络的参数
n_hidden_1 = 784*2# 隐层1的神经元个数
n_input = 784 # MNIST数据集的输出(img shape: 28*28)
n_output=10

# tf Graph input (only pictures)
X = tf.placeholder("float", [None, n_input])
Y=tf.placeholder('float',[None,10])

weights = {
    'encoder_h1': tf.Variable(tf.random_normal([n_input, n_hidden_1])),
    'decoder_h1': tf.Variable(tf.random_normal([n_hidden_1, n_input])),
    'softmax_w': tf.Variable(tf.random_normal([n_hidden_1, n_output])),
}
biases = {
    'encoder_b1': tf.Variable(tf.random_normal([n_hidden_1])),
    'decoder_b1': tf.Variable(tf.random_normal([n_input])),
    'softmax_b': tf.Variable(tf.random_normal([n_output])),
}

# 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']))
    # Encoder Hidden layer with sigmoid activation #2
    return layer_1


# Building the decoder
def decoder(x):
    # Decoder 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

    return layer_1

# Construct model
P=0.1
beta=1
encoder_op = encoder(X)
decoder_op = decoder(encoder_op)

Pj=tf.reduce_mean(encoder_op,0)
sparse_cost=tf.reduce_mean(P*tf.log(P/Pj)+(1-P)*tf.log((1-P)/(1-Pj)))

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

# Define loss and optimizer, minimize the squared error
cost = tf.reduce_mean(tf.pow(y_true - y_pred, 2))+sparse_cost*beta
optimizer = tf.train.RMSPropOptimizer(learning_rate).minimize(cost)
# Initializing the variables
init = tf.global_variables_initializer()

sess = tf.InteractiveSession()
sess.run(init)

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)
        # 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)))
f.show()
plt.draw()

encoder_op = encoder(X)
y_pred=tf.nn.softmax(tf.matmul(encoder(X),weights['softmax_w'])+biases['softmax_b'])
cost = tf.reduce_mean(tf.pow(Y - y_pred, 2))
optimizer = tf.train.RMSPropOptimizer(learning_rate).minimize(cost)

init = tf.global_variables_initializer()

sess = tf.InteractiveSession()
sess.run(init)

total_batch = int(mnist.train.num_examples/batch_size)

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)
        # Run optimization op (backprop) and cost op (to get loss value)
        _, c = sess.run([optimizer, cost], feed_dict={X: batch_xs,Y:batch_ys})
    # Display logs per epoch step
    if epoch % display_step == 0:
        print("Epoch:", '%04d' % (epoch+1),
              "cost=", "{:.9f}".format(c))

print("Optimization Finished!")

注：代码中添加最后添加了softmax分类，并且只有一层隐层，可以注释掉直接运行。这是代码运行后的结果
这里写图片描述

三、自编码的TensorFlow代码

from __future__ import division, print_function, absolute_import

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

# 下载并导入MNIST数据集
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data", one_hot=True)

# 参数
learning_rate = 0.01#学习率
training_epochs = 20#训练的周期
batch_size = 256#每一批次训练的大小
display_step = 1
examples_to_show = 10

# 神经网络的参数
n_hidden_1 = 256 # 隐层1的神经元个数
n_hidden_2 = 128 # 隐层2神经元个数
n_input = 784 # MNIST数据集的输出(img shape: 28*28)
n_output=10

# tf Graph input (only pictures)
X = tf.placeholder("float", [None, n_input])
Y=tf.placeholder('float',[None,10])


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])),
    'softmax_w': tf.Variable(tf.random_normal([n_hidden_2, n_output])),
}
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])),
    'softmax_b': tf.Variable(tf.random_normal([n_output])),
}

# 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']))
    # Encoder 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):
    # Decoder 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)
decoder_op = decoder(encoder_op)

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

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

# Initializing the variables
init = tf.global_variables_initializer()

sess = tf.InteractiveSession()
sess.run(init)

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)
        # 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)))
f.show()
plt.draw()

encoder_op = encoder(X)
y_pred=tf.nn.softmax(tf.matmul(encoder(X),weights['softmax_w'])+biases['softmax_b'])
cost = tf.reduce_mean(tf.pow(Y - y_pred, 2))
optimizer = tf.train.RMSPropOptimizer(learning_rate).minimize(cost)

init = tf.global_variables_initializer()

sess = tf.InteractiveSession()
sess.run(init)

total_batch = int(mnist.train.num_examples/batch_size)

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)
        # Run optimization op (backprop) and cost op (to get loss value)
        _, c = sess.run([optimizer, cost], feed_dict={X: batch_xs,Y:batch_ys})
    # Display logs per epoch step
    if epoch % display_step == 0:
        print("Epoch:", '%04d' % (epoch+1),
              "cost=", "{:.9f}".format(c))

print("Optimization Finished!")