import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow.keras.layers import Input, Dense, Lambda from tensorflow.keras.models import Model from tensorflow.keras import backend as K from tensorflow.keras.datasets import mnist # Daten laden und vorverarbeiten (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-Parameter input_dim = 784 intermediate_dim = 256 latent_dim = 2 batch_size = 100 epochs = 50 # Encoder inputs = Input(shape=(input_dim,)) h = Dense(intermediate_dim, activation='relu')(inputs) z_mean = Dense(latent_dim)(h) z_log_sigma = Dense(latent_dim)(h) def sampling(args): z_mean, z_log_sigma = 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_sigma) * epsilon z = Lambda(sampling)([z_mean, z_log_sigma]) # Decoder decoder_h = Dense(intermediate_dim, activation='relu') decoder_mean = Dense(input_dim, activation='sigmoid') h_decoded = decoder_h(z) x_decoded_mean = decoder_mean(h_decoded) # VAE-Modell vae = Model(inputs, x_decoded_mean) # Verlustfunktion und Modellkompilierung xent_loss = input_dim * tf.keras.losses.binary_crossentropy(inputs, x_decoded_mean) kl_loss = - 0.5 * K.sum(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1) vae_loss = K.mean(xent_loss + kl_loss) vae.add_loss(vae_loss) vae.compile(optimizer='rmsprop') # VAE-Training vae.fit(x_train, x_train, shuffle=True, epochs=epochs, batch_size=batch_size, validation_data=(x_test, x_test)) # Latenten Raum und rekonstruierte Bilder visualisieren encoder = Model(inputs, z_mean) 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.title("Latenter Raum des VAE") plt.xlabel("Dimension 1") plt.ylabel("Dimension 2") plt.savefig("VAE_latent_space.svg") plt.show() 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) n = 15 digit_size = 28 figure = np.zeros((digit_size * n, digit_size * n)) grid_x = np.linspace(-4, 4, n) grid_y = np.linspace(-4, 4, 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) plt.title("Rekonstruktion des VAE über den latenten Raum") plt.xlabel("Dimension 1 des latenten Raums") plt.ylabel("Dimension 2 des latenten Raums") plt.show()