El codificador automático variacional fue propuesto en 2013 por Knigma y Welling en Google y Qualcomm. Un autocodificador variacional (VAE) proporciona una forma probabilística de describir una observación en el espacio latente. Por lo tanto, en lugar de construir un codificador que genere un solo valor para describir cada atributo de estado latente, formularemos nuestro codificador para describir una distribución de probabilidad para cada atributo latente.
Tiene muchas aplicaciones, como la compresión de datos, la creación de datos sintéticos, etc.
Arquitectura:
Los codificadores automáticos son un tipo de red neuronal que aprende las codificaciones de datos del conjunto de datos sin supervisión. Básicamente contiene dos partes: la primera es un codificador que es similar a la red neuronal de convolución excepto por la última capa. El objetivo del codificador es aprender la codificación de datos eficiente del conjunto de datos y pasarlo a una arquitectura de cuello de botella. La otra parte del codificador automático es un decodificador que utiliza el espacio latente en la capa de cuello de botella para regenerar imágenes similares al conjunto de datos. Estos resultados se retropropagan desde la red neuronal en forma de función de pérdida.
El codificador automático variacional se diferencia del codificador automático en que proporciona una manera estadística de describir las muestras del conjunto de datos en el espacio latente. Por lo tanto, en el codificador automático variacional, el codificador genera una distribución de probabilidad en la capa de cuello de botella en lugar de un único valor de salida.
Matemáticas detrás del codificador automático variacional:
El codificador automático variacional usa la divergencia KL como su función de pérdida, el objetivo de esto es minimizar la diferencia entre una supuesta distribución y la distribución original del conjunto de datos.
Supongamos que tenemos una distribución z y queremos generar la observación x a partir de ella. En otras palabras, queremos calcular
Podemos hacerlo de la siguiente manera:
Pero, el cálculo de p(x) puede ser bastante difícil
Esto por lo general hace que sea una distribución intratable. Por lo tanto, necesitamos aproximar p(z|x) a q(z|x) para que sea una distribución manejable. Para aproximar mejor p(z|x) a q(z|x), minimizaremos la pérdida de divergencia KL que calcula qué tan similares son dos distribuciones:
Simplificando, el problema de minimización anterior es equivalente al siguiente problema de maximización:
El primer término representa la probabilidad de reconstrucción y el otro término asegura que nuestra distribución aprendida q es similar a la verdadera distribución previa p.
Por lo tanto, nuestra pérdida total consta de dos términos, uno es el error de reconstrucción y el otro es la pérdida por divergencia KL:
Implementación:
En esta implementación, utilizaremos el conjunto de datos Fashion-MNIST, este conjunto de datos ya está disponible en la API keras.datasets, por lo que no es necesario agregarlo o cargarlo manualmente.
- Primero, necesitamos importar los paquetes necesarios a nuestro entorno de python. Usaremos el paquete Keras con tensorflow como backend.
Código:
python3
# code import numpy as np import tensorflow as tf from tensorflow import keras from tensorflow.keras import Input, Model from tensorflow.keras.layers import Layer, Conv2D, Flatten, Dense, Reshape, Conv2DTranspose import matplotlib.pyplot as plt
- Para los codificadores automáticos variacionales, necesitamos definir la arquitectura de codificador y decodificador de dos partes, pero primero, definiremos la capa de cuello de botella de la arquitectura, la capa de muestreo.
Código:
python3
# this sampling layer is the bottleneck layer of variational autoencoder, # it uses the output from two dense layers z_mean and z_log_var as input, # convert them into normal distribution and pass them to the decoder layer class Sampling(Layer): def call(self, inputs): z_mean, z_log_var = inputs batch = tf.shape(z_mean)[0] dim = tf.shape(z_mean)[1] epsilon = tf.keras.backend.random_normal(shape =(batch, dim)) return z_mean + tf.exp(0.5 * z_log_var) * epsilon
- Ahora, definimos la arquitectura de la parte del codificador de nuestro codificador automático, esta parte toma imágenes como entrada y codifica su representación en la capa de muestreo.
Código:
python3
# Define Encoder Model latent_dim = 2 encoder_inputs = Input(shape =(28, 28, 1)) x = Conv2D(32, 3, activation ="relu", strides = 2, padding ="same")(encoder_inputs) x = Conv2D(64, 3, activation ="relu", strides = 2, padding ="same")(x) x = Flatten()(x) x = Dense(16, activation ="relu")(x) z_mean = Dense(latent_dim, name ="z_mean")(x) z_log_var = Dense(latent_dim, name ="z_log_var")(x) z = Sampling()([z_mean, z_log_var]) encoder = Model(encoder_inputs, [z_mean, z_log_var, z], name ="encoder") encoder.summary()
Model: "encoder"
__________________________________________________________________________________________________
Layer (type) Output Shape Param # Connected to
==================================================================================================
input_3 (InputLayer) [(None, 28, 28, 1)] 0
__________________________________________________________________________________________________
conv2d_2 (Conv2D) (None, 14, 14, 32) 320 input_3[0][0]
__________________________________________________________________________________________________
conv2d_3 (Conv2D) (None, 7, 7, 64) 18496 conv2d_2[0][0]
__________________________________________________________________________________________________
flatten_1 (Flatten) (None, 3136) 0 conv2d_3[0][0]
__________________________________________________________________________________________________
dense_2 (Dense) (None, 16) 50192 flatten_1[0][0]
__________________________________________________________________________________________________
z_mean (Dense) (None, 2) 34 dense_2[0][0]
__________________________________________________________________________________________________
z_log_var (Dense) (None, 2) 34 dense_2[0][0]
__________________________________________________________________________________________________
sampling_1 (Sampling) (None, 2) 0 z_mean[0][0]
z_log_var[0][0]
==================================================================================================
Total params: 69, 076
Trainable params: 69, 076
Non-trainable params: 0
__________________________________________________________________________________________________
- Ahora, definimos la arquitectura de la parte del decodificador de nuestro autocodificador, esta parte toma la salida de la capa de muestreo como entrada y genera una imagen de tamaño (28, 28, 1).
Código:
python3
# Define Decoder Architecture latent_inputs = keras.Input(shape =(latent_dim, )) x = Dense(7 * 7 * 64, activation ="relu")(latent_inputs) x = Reshape((7, 7, 64))(x) x = Conv2DTranspose(64, 3, activation ="relu", strides = 2, padding ="same")(x) x = Conv2DTranspose(32, 3, activation ="relu", strides = 2, padding ="same")(x) decoder_outputs = Conv2DTranspose(1, 3, activation ="sigmoid", padding ="same")(x) decoder = Model(latent_inputs, decoder_outputs, name ="decoder") decoder.summary()
Model: "decoder" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= input_4 (InputLayer) [(None, 2)] 0 _________________________________________________________________ dense_3 (Dense) (None, 3136) 9408 _________________________________________________________________ reshape_1 (Reshape) (None, 7, 7, 64) 0 _________________________________________________________________ conv2d_transpose_3 (Conv2DTr (None, 14, 14, 64) 36928 _________________________________________________________________ conv2d_transpose_4 (Conv2DTr (None, 28, 28, 32) 18464 _________________________________________________________________ conv2d_transpose_5 (Conv2DTr (None, 28, 28, 1) 289 ================================================================= Total params: 65, 089 Trainable params: 65, 089 Non-trainable params: 0 _________________________________________________________________
- En este paso, combinamos el modelo y definimos el procedimiento de entrenamiento con funciones de pérdida.
Código:
python3
# this class takes encoder and decoder models and
# define the complete variational autoencoder architecture
class VAE(keras.Model):
def __init__(self, encoder, decoder, **kwargs):
super(VAE, self).__init__(**kwargs)
self.encoder = encoder
self.decoder = decoder
def train_step(self, data):
if isinstance(data, tuple):
data = data[0]
with tf.GradientTape() as tape:
z_mean, z_log_var, z = encoder(data)
reconstruction = decoder(z)
reconstruction_loss = tf.reduce_mean(
keras.losses.binary_crossentropy(data, reconstruction)
)
reconstruction_loss *= 28 * 28
kl_loss = 1 + z_log_var - tf.square(z_mean) - tf.exp(z_log_var)
kl_loss = tf.reduce_mean(kl_loss)
kl_loss *= -0.5
total_loss = reconstruction_loss + kl_loss
grads = tape.gradient(total_loss, self.trainable_weights)
self.optimizer.apply_gradients(zip(grads, self.trainable_weights))
return {
"loss": total_loss,
"reconstruction_loss": reconstruction_loss,
"kl_loss": kl_loss,
}
- Ahora es el momento adecuado para entrenar nuestro modelo de codificador automático variacional, lo entrenaremos durante 100 épocas. Pero primero necesitamos importar el conjunto de datos MNIST de moda.
Código:
python3
# load fashion mnist dataset from keras.dataset API
(x_train, _), (x_test, _) = keras.datasets.fashion_mnist.load_data()
fmnist_images = np.concatenate([x_train, x_test], axis = 0)
# expand dimension to add a color map dimension
fmnist_images = np.expand_dims(fmnist_images, -1).astype("float32") / 255
# compile and train the model
vae = VAE(encoder, decoder)
vae.compile(optimizer ='rmsprop')
vae.fit(fmnist_images, epochs = 100, batch_size = 64)
Epoch 1/100 1094/1094 [==============================] - 7s 6ms/step - loss: 301.9441 - reconstruction_loss: 298.3138 - kl_loss: 3.6303 Epoch 2/100 1094/1094 [==============================] - 7s 6ms/step - loss: 273.5940 - reconstruction_loss: 270.0484 - kl_loss: 3.5456 Epoch 3/100 1094/1094 [==============================] - 7s 6ms/step - loss: 269.3337 - reconstruction_loss: 265.9077 - kl_loss: 3.4260 Epoch 4/100 1094/1094 [==============================] - 7s 6ms/step - loss: 266.8168 - reconstruction_loss: 263.4100 - kl_loss: 3.4068 Epoch 5/100 1094/1094 [==============================] - 7s 6ms/step - loss: 264.9917 - reconstruction_loss: 261.5603 - kl_loss: 3.4314 Epoch 6/100 1094/1094 [==============================] - 7s 6ms/step - loss: 263.5237 - reconstruction_loss: 260.0712 - kl_loss: 3.4525 Epoch 7/100 1094/1094 [==============================] - 7s 6ms/step - loss: 262.3414 - reconstruction_loss: 258.8548 - kl_loss: 3.4865 Epoch 8/100 1094/1094 [==============================] - 7s 6ms/step - loss: 261.4241 - reconstruction_loss: 257.9104 - kl_loss: 3.5137 Epoch 9/100 1094/1094 [==============================] - 7s 6ms/step - loss: 260.6090 - reconstruction_loss: 257.0662 - kl_loss: 3.5428 Epoch 10/100 1094/1094 [==============================] - 7s 6ms/step - loss: 259.9735 - reconstruction_loss: 256.4075 - kl_loss: 3.5660 Epoch 11/100 1094/1094 [==============================] - 7s 6ms/step - loss: 259.4184 - reconstruction_loss: 255.8348 - kl_loss: 3.5836 Epoch 12/100 1094/1094 [==============================] - 7s 6ms/step - loss: 258.9688 - reconstruction_loss: 255.3724 - kl_loss: 3.5964 Epoch 13/100 1094/1094 [==============================] - 7s 6ms/step - loss: 258.5413 - reconstruction_loss: 254.9356 - kl_loss: 3.6057 Epoch 14/100 1094/1094 [==============================] - 7s 6ms/step - loss: 258.2400 - reconstruction_loss: 254.6236 - kl_loss: 3.6163 Epoch 15/100 1094/1094 [==============================] - 7s 6ms/step - loss: 257.9335 - reconstruction_loss: 254.3038 - kl_loss: 3.6298 Epoch 16/100 1094/1094 [==============================] - 7s 6ms/step - loss: 257.6331 - reconstruction_loss: 253.9993 - kl_loss: 3.6339 Epoch 17/100 1094/1094 [==============================] - 7s 6ms/step - loss: 257.4199 - reconstruction_loss: 253.7707 - kl_loss: 3.6492 Epoch 18/100 1094/1094 [==============================] - 6s 6ms/step - loss: 257.1951 - reconstruction_loss: 253.5309 - kl_loss: 3.6643 Epoch 19/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.9326 - reconstruction_loss: 253.2723 - kl_loss: 3.6604 Epoch 20/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.7551 - reconstruction_loss: 253.0836 - kl_loss: 3.6715 Epoch 21/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.5663 - reconstruction_loss: 252.8877 - kl_loss: 3.6786 Epoch 22/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.4068 - reconstruction_loss: 252.7112 - kl_loss: 3.6956 Epoch 23/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.2588 - reconstruction_loss: 252.5588 - kl_loss: 3.7000 Epoch 24/100 1094/1094 [==============================] - 7s 6ms/step - loss: 256.0853 - reconstruction_loss: 252.3794 - kl_loss: 3.7059 Epoch 25/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.9321 - reconstruction_loss: 252.2201 - kl_loss: 3.7120 Epoch 26/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.7962 - reconstruction_loss: 252.0814 - kl_loss: 3.7148 Epoch 27/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.6953 - reconstruction_loss: 251.9673 - kl_loss: 3.7280 Epoch 28/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.5534 - reconstruction_loss: 251.8248 - kl_loss: 3.7287 Epoch 29/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.4437 - reconstruction_loss: 251.7134 - kl_loss: 3.7303 Epoch 30/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.3439 - reconstruction_loss: 251.6064 - kl_loss: 3.7375 Epoch 31/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.2326 - reconstruction_loss: 251.5018 - kl_loss: 3.7308 Epoch 32/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.1356 - reconstruction_loss: 251.3933 - kl_loss: 3.7423 Epoch 33/100 1094/1094 [==============================] - 7s 6ms/step - loss: 255.0660 - reconstruction_loss: 251.3224 - kl_loss: 3.7436 Epoch 34/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.9977 - reconstruction_loss: 251.2449 - kl_loss: 3.7528 Epoch 35/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.8857 - reconstruction_loss: 251.1363 - kl_loss: 3.7494 Epoch 36/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.7980 - reconstruction_loss: 251.0481 - kl_loss: 3.7499 Epoch 37/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.7485 - reconstruction_loss: 250.9851 - kl_loss: 3.7634 Epoch 38/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.6701 - reconstruction_loss: 250.9049 - kl_loss: 3.7652 Epoch 39/100 1094/1094 [==============================] - 6s 6ms/step - loss: 254.6105 - reconstruction_loss: 250.8389 - kl_loss: 3.7716 Epoch 40/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.4979 - reconstruction_loss: 250.7333 - kl_loss: 3.7646 Epoch 41/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.4734 - reconstruction_loss: 250.7037 - kl_loss: 3.7697 Epoch 42/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.4408 - reconstruction_loss: 250.6576 - kl_loss: 3.7831 Epoch 43/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.3272 - reconstruction_loss: 250.5562 - kl_loss: 3.7711 Epoch 44/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.3110 - reconstruction_loss: 250.5354 - kl_loss: 3.7755 Epoch 45/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.1982 - reconstruction_loss: 250.4256 - kl_loss: 3.7726 Epoch 46/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.1655 - reconstruction_loss: 250.3795 - kl_loss: 3.7860 Epoch 47/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.0979 - reconstruction_loss: 250.3105 - kl_loss: 3.7875 Epoch 48/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.0801 - reconstruction_loss: 250.2973 - kl_loss: 3.7828 Epoch 49/100 1094/1094 [==============================] - 7s 6ms/step - loss: 254.0101 - reconstruction_loss: 250.2270 - kl_loss: 3.7831 Epoch 50/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.9512 - reconstruction_loss: 250.1681 - kl_loss: 3.7831 Epoch 51/100 1094/1094 [==============================] - 7s 7ms/step - loss: 253.9307 - reconstruction_loss: 250.1408 - kl_loss: 3.7899 Epoch 52/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.8858 - reconstruction_loss: 250.1059 - kl_loss: 3.7800 Epoch 53/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.8118 - reconstruction_loss: 250.0236 - kl_loss: 3.7882 Epoch 54/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.8171 - reconstruction_loss: 250.0325 - kl_loss: 3.7845 Epoch 55/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.7622 - reconstruction_loss: 249.9735 - kl_loss: 3.7887 Epoch 56/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.7338 - reconstruction_loss: 249.9380 - kl_loss: 3.7959 Epoch 57/100 1094/1094 [==============================] - 6s 6ms/step - loss: 253.6761 - reconstruction_loss: 249.8792 - kl_loss: 3.7969 Epoch 58/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.6236 - reconstruction_loss: 249.8283 - kl_loss: 3.7954 Epoch 59/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.6181 - reconstruction_loss: 249.8236 - kl_loss: 3.7945 Epoch 60/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.5509 - reconstruction_loss: 249.7587 - kl_loss: 3.7921 Epoch 61/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.5124 - reconstruction_loss: 249.7126 - kl_loss: 3.7998 Epoch 62/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.4739 - reconstruction_loss: 249.6683 - kl_loss: 3.8056 Epoch 63/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.4609 - reconstruction_loss: 249.6567 - kl_loss: 3.8042 Epoch 64/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.4066 - reconstruction_loss: 249.6020 - kl_loss: 3.8045 Epoch 65/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.3578 - reconstruction_loss: 249.5580 - kl_loss: 3.7998 Epoch 66/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.3728 - reconstruction_loss: 249.5609 - kl_loss: 3.8118 Epoch 67/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.3523 - reconstruction_loss: 249.5351 - kl_loss: 3.8171 Epoch 68/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.2646 - reconstruction_loss: 249.4452 - kl_loss: 3.8194 Epoch 69/100 1094/1094 [==============================] - 6s 6ms/step - loss: 253.2642 - reconstruction_loss: 249.4603 - kl_loss: 3.8040 Epoch 70/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.2227 - reconstruction_loss: 249.4159 - kl_loss: 3.8068 Epoch 71/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.1848 - reconstruction_loss: 249.3755 - kl_loss: 3.8094 Epoch 72/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.1812 - reconstruction_loss: 249.3737 - kl_loss: 3.8074 Epoch 73/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.1803 - reconstruction_loss: 249.3743 - kl_loss: 3.8059 Epoch 74/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.1295 - reconstruction_loss: 249.3114 - kl_loss: 3.8181 Epoch 75/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.0516 - reconstruction_loss: 249.2391 - kl_loss: 3.8125 Epoch 76/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.0736 - reconstruction_loss: 249.2582 - kl_loss: 3.8154 Epoch 77/100 1094/1094 [==============================] - 6s 6ms/step - loss: 253.0331 - reconstruction_loss: 249.2200 - kl_loss: 3.8131 Epoch 78/100 1094/1094 [==============================] - 7s 6ms/step - loss: 253.0479 - reconstruction_loss: 249.2272 - kl_loss: 3.8207 Epoch 79/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.9317 - reconstruction_loss: 249.1137 - kl_loss: 3.8179 Epoch 80/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.9578 - reconstruction_loss: 249.1483 - kl_loss: 3.8095 Epoch 81/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.9072 - reconstruction_loss: 249.0963 - kl_loss: 3.8109 Epoch 82/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.8793 - reconstruction_loss: 249.0646 - kl_loss: 3.8147 Epoch 83/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.8914 - reconstruction_loss: 249.0676 - kl_loss: 3.8238 Epoch 84/100 1094/1094 [==============================] - 6s 6ms/step - loss: 252.8365 - reconstruction_loss: 249.0121 - kl_loss: 3.8244 Epoch 85/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.8063 - reconstruction_loss: 248.9844 - kl_loss: 3.8218 Epoch 86/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.7960 - reconstruction_loss: 248.9777 - kl_loss: 3.8183 Epoch 87/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.7733 - reconstruction_loss: 248.9529 - kl_loss: 3.8204 Epoch 88/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.7303 - reconstruction_loss: 248.9055 - kl_loss: 3.8248 Epoch 89/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.7225 - reconstruction_loss: 248.8902 - kl_loss: 3.8323 Epoch 90/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.6822 - reconstruction_loss: 248.8549 - kl_loss: 3.8273 Epoch 91/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.6540 - reconstruction_loss: 248.8314 - kl_loss: 3.8227 Epoch 92/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.6540 - reconstruction_loss: 248.8239 - kl_loss: 3.8300 Epoch 93/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.6213 - reconstruction_loss: 248.7778 - kl_loss: 3.8435 Epoch 94/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.5990 - reconstruction_loss: 248.7594 - kl_loss: 3.8397 Epoch 95/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.5786 - reconstruction_loss: 248.7413 - kl_loss: 3.8373 Epoch 96/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.5839 - reconstruction_loss: 248.7411 - kl_loss: 3.8427 Epoch 97/100 1094/1094 [==============================] - 7s 7ms/step - loss: 252.5364 - reconstruction_loss: 248.6960 - kl_loss: 3.8404 Epoch 98/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.5347 - reconstruction_loss: 248.6915 - kl_loss: 3.8431 Epoch 99/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.4996 - reconstruction_loss: 248.6569 - kl_loss: 3.8428 Epoch 100/100 1094/1094 [==============================] - 7s 6ms/step - loss: 252.4938 - reconstruction_loss: 248.6405 - kl_loss: 3.8533 <tensorflow.python.keras.callbacks.History at 0x7f5467c56be0>
- En este paso, mostramos los resultados del entrenamiento, mostraremos estos resultados según sus valores en vectores espaciales latentes.
Código:
python3
def plot_latent(encoder, decoder):
# display a n * n 2D manifold of images
n = 10
img_dim = 28
scale = 2.0
figsize = 15
figure = np.zeros((img_dim * n, img_dim * n))
# linearly spaced coordinates corresponding to the 2D plot
# of images classes in the latent space
grid_x = np.linspace(-scale, scale, n)
grid_y = np.linspace(-scale, scale, n)[::-1]
for i, yi in enumerate(grid_y):
for j, xi in enumerate(grid_x):
z_sample = np.array([[xi, yi]])
x_decoded = decoder.predict(z_sample)
images = x_decoded[0].reshape(img_dim, img_dim)
figure[
i * img_dim : (i + 1) * img_dim,
j * img_dim : (j + 1) * img_dim,
] = images
plt.figure(figsize =(figsize, figsize))
start_range = img_dim // 2
end_range = n * img_dim + start_range + 1
pixel_range = np.arange(start_range, end_range, img_dim)
sample_range_x = np.round(grid_x, 1)
sample_range_y = np.round(grid_y, 1)
plt.xticks(pixel_range, sample_range_x)
plt.yticks(pixel_range, sample_range_y)
plt.xlabel("z[0]")
plt.ylabel("z[1]")
plt.imshow(figure, cmap ="Greys_r")
plt.show()
plot_latent(encoder, decoder)
- Para obtener una visión más clara de los valores de nuestros vectores latentes de representación, trazaremos el diagrama de dispersión de los datos de entrenamiento sobre la base de sus valores de las dimensiones latentes correspondientes generadas por el codificador.
Código:
python3
def plot_label_clusters(encoder, decoder, data, test_lab):
z_mean, _, _ = encoder.predict(data)
plt.figure(figsize =(12, 10))
sc = plt.scatter(z_mean[:, 0], z_mean[:, 1], c = test_lab)
cbar = plt.colorbar(sc, ticks = range(10))
cbar.ax.set_yticklabels([labels.get(i) for i in range(10)])
plt.xlabel("z[0]")
plt.ylabel("z[1]")
plt.show()
labels = {0 :"T-shirt / top",
1: "Trouser",
2: "Pullover",
3: "Dress",
4: "Coat",
5: "Sandal",
6: "Shirt",
7: "Sneaker",
8: "Bag",
9: "Ankle boot"}
(x_train, y_train), _ = keras.datasets.fashion_mnist.load_data()
x_train = np.expand_dims(x_train, -1).astype("float32") / 255
plot_label_clusters(encoder, decoder, x_train, y_train)
Referencias: