10. Reconsturcting Inputs using Autoencoders/10.03 Reconstructing MNIST images using Autoencoder.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconstructing MNIST images using Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have understood how autoencoders reconstruct the inputs, in this section we will learn how autoencoders reconstruct the images of handwritten digits using the MNIST dataset. \n",
    "\n",
    "\n",
    "In this chapter, we use keras API from the tensorflow for building the models. So that we would be familiarized with how to use high-level APIs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Libraries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let us import the necessary libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "from tensorflow.keras.models import Model\n",
    "from tensorflow.keras.layers import Input, Dense\n",
    "\n",
    "import tensorflow as tf\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)\n",
    "\n",
    "#plotting\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "#dataset\n",
    "from tensorflow.keras.datasets import mnist\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare the Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us load the MNIST dataset. We don't need the labels for autoencoder. Since we are reconstructing the given input we don't need the labels. So, we just load x_train for training and x_test for testing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, _), (x_test, _) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the data by dividing with max pixel value which is 255:"
   ]
  },
  {
   "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": [
    "Shape of our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((60000, 28, 28), (10000, 28, 28))\n"
     ]
    }
   ],
   "source": [
    "print(x_train.shape, x_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape the images as 2D array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 6,
   "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": [
    "# Define the Encoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we define the encoder which takes the images as an input and returns the encodings. \n",
    "\n",
    "Define the size of the encodings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoding_dim = 32"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the placeholders for the input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_image = Input(shape=(784,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Define the encoder which takes the input_image and returns the encodings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoder  = Dense(encoding_dim, activation='relu')(input_image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define the Decoder\n",
    "\n",
    "Let us define the decoder which takes the encoded values from the encoder and returns the reconstructed image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "decoder = Dense(784, activation='sigmoid')(encoder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Build the model\n",
    "\n",
    "Now that we defined encoder and decoder, we define the model which takes images as input and returns the output of the decoder which is the reconstructed image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model(inputs=input_image, outputs=decoder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at summary of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 32)                25120     \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 784)               25872     \n",
      "=================================================================\n",
      "Total params: 50,992\n",
      "Trainable params: 50,992\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compile the model with loss as binary cross entropy and we minimize the loss using AdaDelta optimizer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer='adadelta', loss='binary_crossentropy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let us train the model.\n",
    "\n",
    "Generally, we feed the data to the model as model.fit(x,y) where x is the input and y is the label. But since autoencoders reconstruct its inputs, the input and output to the model should be the same. So we feed the data to the model as model.fit(x_train, x_train)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/50\n",
      "60000/60000 [==============================] - 4s 72us/sample - loss: 0.3566 - val_loss: 0.2724\n",
      "Epoch 2/50\n",
      "60000/60000 [==============================] - 3s 43us/sample - loss: 0.2668 - val_loss: 0.2580\n",
      "Epoch 3/50\n",
      "60000/60000 [==============================] - 2s 40us/sample - loss: 0.2468 - val_loss: 0.2327\n",
      "Epoch 4/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.2239 - val_loss: 0.2132\n",
      "Epoch 5/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.2078 - val_loss: 0.2001\n",
      "Epoch 6/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1969 - val_loss: 0.1911\n",
      "Epoch 7/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1888 - val_loss: 0.1837\n",
      "Epoch 8/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1820 - val_loss: 0.1775\n",
      "Epoch 9/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1759 - val_loss: 0.1717\n",
      "Epoch 10/50\n",
      "60000/60000 [==============================] - 2s 41us/sample - loss: 0.1704 - val_loss: 0.1666\n",
      "Epoch 11/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1656 - val_loss: 0.1621\n",
      "Epoch 12/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1613 - val_loss: 0.1579\n",
      "Epoch 13/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1574 - val_loss: 0.1541\n",
      "Epoch 14/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1537 - val_loss: 0.1506\n",
      "Epoch 15/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1504 - val_loss: 0.1474\n",
      "Epoch 16/50\n",
      "60000/60000 [==============================] - 2s 40us/sample - loss: 0.1473 - val_loss: 0.1444\n",
      "Epoch 17/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1444 - val_loss: 0.1415\n",
      "Epoch 18/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1417 - val_loss: 0.1389\n",
      "Epoch 19/50\n",
      "60000/60000 [==============================] - 3s 55us/sample - loss: 0.1392 - val_loss: 0.1364\n",
      "Epoch 20/50\n",
      "60000/60000 [==============================] - 3s 50us/sample - loss: 0.1367 - val_loss: 0.1341\n",
      "Epoch 21/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1344 - val_loss: 0.1317\n",
      "Epoch 22/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1322 - val_loss: 0.1295\n",
      "Epoch 23/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1300 - val_loss: 0.1274\n",
      "Epoch 24/50\n",
      "60000/60000 [==============================] - 2s 41us/sample - loss: 0.1280 - val_loss: 0.1254\n",
      "Epoch 25/50\n",
      "60000/60000 [==============================] - 3s 43us/sample - loss: 0.1261 - val_loss: 0.1236\n",
      "Epoch 26/50\n",
      "60000/60000 [==============================] - 2s 40us/sample - loss: 0.1242 - val_loss: 0.1217\n",
      "Epoch 27/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1225 - val_loss: 0.1201\n",
      "Epoch 28/50\n",
      "60000/60000 [==============================] - 3s 45us/sample - loss: 0.1209 - val_loss: 0.1185\n",
      "Epoch 29/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1194 - val_loss: 0.1170\n",
      "Epoch 30/50\n",
      "60000/60000 [==============================] - 2s 40us/sample - loss: 0.1179 - val_loss: 0.1156\n",
      "Epoch 31/50\n",
      "60000/60000 [==============================] - 3s 42us/sample - loss: 0.1166 - val_loss: 0.1144\n",
      "Epoch 32/50\n",
      "60000/60000 [==============================] - 2s 41us/sample - loss: 0.1154 - val_loss: 0.1131\n",
      "Epoch 33/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1142 - val_loss: 0.1120\n",
      "Epoch 34/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1132 - val_loss: 0.1110\n",
      "Epoch 35/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1122 - val_loss: 0.1101\n",
      "Epoch 36/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1113 - val_loss: 0.1092\n",
      "Epoch 37/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1104 - val_loss: 0.1083\n",
      "Epoch 38/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1096 - val_loss: 0.1076\n",
      "Epoch 39/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1089 - val_loss: 0.1069\n",
      "Epoch 40/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1082 - val_loss: 0.1062\n",
      "Epoch 41/50\n",
      "60000/60000 [==============================] - 2s 41us/sample - loss: 0.1075 - val_loss: 0.1056\n",
      "Epoch 42/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1069 - val_loss: 0.1050\n",
      "Epoch 43/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1064 - val_loss: 0.1045\n",
      "Epoch 44/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1058 - val_loss: 0.1040\n",
      "Epoch 45/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1053 - val_loss: 0.1035\n",
      "Epoch 46/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1049 - val_loss: 0.1030\n",
      "Epoch 47/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1044 - val_loss: 0.1026\n",
      "Epoch 48/50\n",
      "60000/60000 [==============================] - 2s 38us/sample - loss: 0.1040 - val_loss: 0.1022\n",
      "Epoch 49/50\n",
      "60000/60000 [==============================] - 2s 39us/sample - loss: 0.1036 - val_loss: 0.1019\n",
      "Epoch 50/50\n",
      "60000/60000 [==============================] - ETA: 0s - loss: 0.103 - 2s 38us/sample - loss: 0.1033 - val_loss: 0.1015\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f8eeaffd710>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x_train, x_train, epochs=50, batch_size=256, shuffle=True, validation_data=(x_test, x_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reconstruct images\n",
    "\n",
    "Let us see how our model is performing in the test dataset. Feed the test images to the model and get the reconstructed images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "reconstructed_images = model.predict(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting reconstructed images\n",
    "\n",
    "\n",
    "First let us plot the atcual images i.e input images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 7\n",
    "plt.figure(figsize=(20, 4))\n",
    "for i in range(n):\n",
    " \n",
    "    ax = plt.subplot(1, n, i+1)\n",
    "    plt.imshow(x_test[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the reconstructed image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 7\n",
    "plt.figure(figsize=(20, 4))\n",
    "for i in range(n):\n",
    "    ax = plt.subplot(2, n, i + n + 1)\n",
    "    plt.imshow(reconstructed_images[i].reshape(28, 28))\n",
    "    plt.gray()\n",
    "    ax.get_xaxis().set_visible(False)\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can notice, autoencoders have learned to reconstruct the given input image. In the next section, we will learn about convolutional autoencoder which uses convolutional layers in the encoder and decoder network. "
   ]
  }
 ],
 "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
}