範例程式研讀。
＊TensorFlow 2.x 動態圖機制Eager Mode可能會導致範例程式拋出SymbolicException錯誤，需手動關閉：
python
tf.compat.v1.disable_eager_execution()超參數與自訂函式
超參數epsilon_std是在sampling()裡面所使用，但keras.backend.random_normal的參數stddev(標準差)預設值就是1.0。
sampling()會在編碼器的結構中接收參數：平均值和對數變異數(z_mean, z_log_var)，返回取樣自平均值=z_mean且標準差=$ \sqrt {z\_log\_var} $之常態分佈的隨機數值陣列，也就是Z(潛在空間，latent space)。
vae_loss()負責在VAE訓練過程接收參數：實際值(原始影像)及預測值(解碼器生成影像)來計算Loss，返回二元交叉熵(binary cross entropy)與相對熵(relative entropy)的和。
python
# defining the key parameters
batch_size = 100
original_dim = 784 # MNIST: 28 * 28
latent_dim = 2
intermediate_dim = 256
epochs = 5
epsilon_std = 1.0
def sampling(args: tuple):
# we grab the variables from the tuple
z_mean, z_log_var = args
epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim), mean=0., stddev=epsilon_std)
return z_mean + K.exp(z_log_var / 2) * epsilon
# defining the losses
def vae_loss(x: tf.Tensor, x_decoded_mean: tf.Tensor):
# cross entropy
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
# relative entropy
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
vae_loss = K.mean(xent_loss + kl_loss)
return vae_loss變分自編碼器模型
Encoder：輸入影像，輸出平均值、對數變異數、潛在空間。
Decoder：輸入潛在空間，輸出生成影像。
python
# defining the encoder
x = Input(shape=(original_dim,), name="input")
h = Dense(intermediate_dim, activation='relu', name="encoding")(x)
# mean of the latent space
z_mean = Dense(latent_dim, name="mean")(h)
# log variance of the latent space
z_log_var = Dense(latent_dim, name="log-variance")(h)
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])
encoder = Model(x, [z_mean, z_log_var, z], name="encoder")
encoder.summary()
# defining the decoder
input_decoder = Input(shape=(latent_dim,), name="decoder_input")
decoder_h = Dense(intermediate_dim, activation='relu', name="decoder_h")(input_decoder)
x_decoded = Dense(original_dim, activation='sigmoid', name="flat_decoded")(decoder_h)
decoder = Model(input_decoder, x_decoded, name="decoder")
decoder.summary()
# defining the VAE
# encoder return: [z_mean, z_log_var, z]
output_combined = decoder(encoder(x)[2])
vae = Model(x, output_combined, name="VAE")
vae.summary()
vae.compile(optimizer='rmsprop', loss=vae_loss)模型訓練
- VAE的輸出也是影像，所以fit()的Y參數要輸入影像資料而非數據標籤。
python
# load data
(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:]))) # (60000, 784)
x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:]))) # (10000, 784)
# training
vae.fit(x_train, x_train, shuffle=True, epochs=epochs, batch_size=batch_size)散點圖
測試資料經編碼後於潛在空間中的分佈情形
我另外畫出後續會用來採樣生成圖片的紅框區域
python
# display a 2D plot of the digit classes in the latent space
x_test_encoded = encoder.predict(x_test, batch_size=batch_size)[0]
fig = plt.figure(figsize=(6, 6))
plt.scatter(x_test_encoded[:,0], x_test_encoded[:,1], c=y_test, cmap='viridis')
plt.colorbar()
plt.show()生成圖片
使用numpy.linspace()生成區間(0.05, 0.95)的具有n個元素的等差數列，再由scipy.stats.norm.ppf()轉換為常態累積分佈的百分位數，做為潛在空間取樣座標(grid_x, grid_y)。
反轉grid_x順序的圖片生成結果，對應散點圖的紅框範圍(原始範例會上下顛倒)
python
# display a 2D manifold of the digits
n = 15 # figure with 15x15 digits
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
# to produce values of the latent variables z, since the prior of the latent space is Gaussian
grid_x = norm.ppf(np.linspace(0.05, 0.95, n))
grid_y = norm.ppf(np.linspace(0.05, 0.95, n))
for i, yi in (enumerate(grid_x)):
for j, xi in enumerate(grid_y):
z_sample = np.array([[xi, yi]])
x_decoded = decoder.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()