生成对抗网络前言（4）——变分自动编码器（Variational autoencoder，VAE）介绍
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
from keras.layers import Input, Dense, Lambda
from keras.models import Model
from keras import backend as K
from keras import metrics
from keras.datasets import mnist
original_dim = 28*28
intermediate_dim = 64
latent_dim = 2
batch_size = 32
x = Input(shape=(original_dim,))
h = Dense(intermediate_dim, activation='relu')(x)
z_mean = Dense(latent_dim)(h)
z_log_var = Dense(latent_dim)(h)
#定义采样函数(采样新的相似点)
def sampling(args):
z_mean, z_log_var = args
epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim), mean=0.,
stddev=0.1)
return z_mean + K.exp(z_log_var / 2) * epsilon
# note that "output_shape" isn't necessary with the TensorFlow backend
# 注意，“output_shape”对于TensorFlow后端不是必需的。
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])
# 将采样得到的点映射回去重构原输出
decoder_h = Dense(intermediate_dim, activation='relu')
decoder_mean = Dense(original_dim, activation='sigmoid')
h_decoded = decoder_h(z)
x_decoded_mean = decoder_mean(h_decoded)
'''
需要实例化三个模型：
- 一个端到端的自动编码器，用于完成输入信号的重构 end-to-end autoencoder
- 一个用于将输入空间映射为隐空间的编码器 encoder, from inputs to latent space
- 一个利用隐空间的分布产生的样本点生成对应重构样本的生成器 generator, from latent space to reconstructed inputs
'''
# 实例化VAE模型(端到端的自动编码器)
vae = Model(x, x_decoded_mean)
# Compute VAE loss
# 计算VAE损失
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)# 均方距离
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)# KL散度
vae_loss = K.mean(xent_loss + kl_loss)
vae.add_loss(vae_loss)
vae.compile(optimizer='rmsprop')
vae.summary()
# 利用MNIST数据集训练VAE
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.
x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))
x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))
vae.fit(x_train,shuffle=True,epochs=100,
batch_size=batch_size,validation_data=(x_test, None))
# encoder, from inputs to latent space
# 建立一个隐空间输入模型(将输入空间映射为隐空间的编码器)
encoder = Model(x, z_mean)
encoder.summary()
# display a 2D plot of the digit classes in the latent space
# 在潜在空间中显示数字类的2D图
x_test_encoded = encoder.predict(x_test, batch_size=batch_size)
plt.figure(figsize=(6, 6))
plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_test)
plt.colorbar()
plt.show()
# 建立一个数字生成器，可以从学习的分布中取样(一个利用隐空间的分布产生的样本点生成对应的重构样本的生成器)
decoder_input = Input(shape=(latent_dim,))
_h_decoded = decoder_h(decoder_input)
_x_decoded_mean = decoder_mean(_h_decoded)
generator = Model(decoder_input, _x_decoded_mean)
generator.summary()
# 生成MNIST数字
n = 15 # figure with 15x15 digits # 15X15数字图形
digit_size = 28
figure = np.zeros((digit_size * n, digit_size * n))
# linearly spaced coordinates on the unit square were transformed through the inverse CDF (ppf) of the Gaussian
# 单位平方的线性间隔坐标通过高斯的逆CDF（ppf）变换。
# to produce values of the latent variables z, since the prior of the latent space is Gaussian
# 产生潜在变量Z的值，因为潜在空间的先验是高斯
# grid_x = ((0.05, 0.95, n))
# grid_y = ((0.05, 0.95, n))
grid_x = np.linspace(-15, 15, n)
grid_y = np.linspace(-15, 15, n)
for i, yi in enumerate(grid_x):
for j, xi in enumerate(grid_y):
z_sample = np.array([[xi, yi]])
x_decoded = generator.predict(z_sample)
digit = x_decoded[0].reshape(digit_size, digit_size)
figure[i * digit_size: (i + 1) * digit_size,
j * digit_size: (j + 1) * digit_size] = digit
plt.figure(figsize=(10, 10))
plt.imshow(figure, cmap='Greys_r')
plt.show()