10. Reconsturcting Inputs using Autoencoders/10.13 Generating images using VAE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating images using VAE\n",
    "\n",
    "Now that we have understood how Variational Autoencoders(VAE) works, in this section we will learn how to use VAE to generate images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Import the required libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "from tensorflow.keras.layers import Input, Dense, Lambda\n",
    "from tensorflow.keras.models import Model\n",
    "from tensorflow.keras import backend as K\n",
    "from tensorflow.keras import metrics\n",
    "from tensorflow.keras.datasets import mnist\n",
    "\n",
    "import tensorflow as tf\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Prepare the dataset\n",
    "\n",
    "Load the MNIST dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, _), (x_test, _) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x_train.astype('float32') / 255.\n",
    "x_test = x_test.astype('float32') / 255."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))\n",
    "x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the shape of data would become:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((60000, 784), (10000, 784))\n"
     ]
    }
   ],
   "source": [
    "print(x_train.shape, x_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's define some important parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "original_dim = 784\n",
    "latent_dim = 2\n",
    "intermediate_dim = 256\n",
    "epochs = 10\n",
    "epsilon_std = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining Encoder\n",
    "\n",
    "\n",
    "Define the input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Input(shape=(original_dim,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the Encoder hidden layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = Dense(intermediate_dim, activation='relu')(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Compute mean and variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_mean = Dense(latent_dim)(h)\n",
    "z_log_var = Dense(latent_dim)(h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Define the sampling operation\n",
    "\n",
    "\n",
    "Define the sampling operation with a reparameterization trick which samples the latent vector form the encoder's distribution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampling(args):\n",
    "    z_mean, z_log_var = args\n",
    "    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim), mean=0., stddev=epsilon_std)\n",
    "    \n",
    "    return z_mean + K.exp(z_log_var / 2) * epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample the latent vector z from the mean and variance of the encoder's distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the Decoder\n",
    "\n",
    "We define the decoder with two layers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "decoder_hidden = Dense(intermediate_dim, activation='relu')\n",
    "decoder_reconstruct = Dense(original_dim, activation='sigmoid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reconstruct images using the decoder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "decoded = decoder_hidden(z)\n",
    "reconstructed = decoder_reconstruct(decoded)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "vae = Model(x, reconstructed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the loss\n",
    "\n",
    "\n",
    "As we learned we use two types of loss: Reconstruction loss and KL divergence loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Reconstuction loss is defined as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "Reconstruction_loss = original_dim * metrics.binary_crossentropy(x, reconstructed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "KL diveregnce loss is defined as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "kl_divergence_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus our total loss becomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_loss = K.mean(Reconstruction_loss + kl_divergence_loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Add loss and compile the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "vae.add_loss(total_loss)\n",
    "vae.compile(optimizer='rmsprop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      " - 7s - loss: 189.6828 - val_loss: 171.2307\n",
      "Epoch 2/10\n",
      " - 6s - loss: 169.0377 - val_loss: 167.7445\n",
      "Epoch 3/10\n",
      " - 6s - loss: 166.3774 - val_loss: 165.3534\n",
      "Epoch 4/10\n",
      " - 6s - loss: 164.3107 - val_loss: 164.0418\n",
      "Epoch 5/10\n",
      " - 7s - loss: 162.7984 - val_loss: 162.3211\n",
      "Epoch 6/10\n",
      " - 7s - loss: 161.6029 - val_loss: 161.3738\n",
      "Epoch 7/10\n",
      " - 7s - loss: 160.5524 - val_loss: 160.5113\n",
      "Epoch 8/10\n",
      " - 7s - loss: 159.5963 - val_loss: 159.8307\n",
      "Epoch 9/10\n",
      " - 7s - loss: 158.7382 - val_loss: 158.5780\n",
      "Epoch 10/10\n",
      " - 7s - loss: 157.9101 - val_loss: 157.8535\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f46e61e3ad0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vae.fit(x_train,shuffle=True, epochs=epochs, batch_size=batch_size,verbose=2, validation_data=(x_test, None))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining Generator\n",
    "\n",
    "Now, we define the generator that samples from the learned distribution and generates an image. Decoder is bascially our generator as it generates the images. Define the two layers of decoder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "decoder_input = Input(shape=(latent_dim,))\n",
    "_decoded = decoder_hidden(decoder_input)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Define the generator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "_reconstructed = decoder_reconstruct(_decoded)\n",
    "generator = Model(decoder_input, _reconstructed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Plotting generated images\n",
    "\n",
    "\n",
    "Now, we plot the image generated by the generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 7 \n",
    "digit_size = 28\n",
    "figure = np.zeros((digit_size * n, digit_size * n))\n",
    "\n",
    "grid_x = norm.ppf(np.linspace(0.05, 0.95, n))\n",
    "grid_y = norm.ppf(np.linspace(0.05, 0.95, n))\n",
    "\n",
    "for i, yi in enumerate(grid_x):\n",
    "    for j, xi in enumerate(grid_y):\n",
    "        z_sample = np.array([[xi, yi]])\n",
    "        x_decoded = generator.predict(z_sample)\n",
    "        digit = x_decoded[0].reshape(digit_size, digit_size)\n",
    "        figure[i * digit_size: (i + 1) * digit_size,\n",
    "               j * digit_size: (j + 1) * digit_size] = digit\n",
    "\n",
    "plt.figure(figsize=(4, 4), dpi=100)\n",
    "plt.imshow(figure, cmap='Greys_r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot shows the generated images by the VAE. Thus, in this chapter, we have learned about several interesting types of autoencoders, in the next chapter we will learn about few-shot learning algorithms."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}