Mnist_VAE.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pawanagr/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "from keras.layers import Input, Dense, Lambda\n",
    "from keras.objectives import binary_crossentropy,mse\n",
    "import numpy as np\n",
    "import random\n",
    "import tensorflow as tf\n",
    "import keras.backend as K\n",
    "import matplotlib.pyplot as plt\n",
    "from keras.models import Model\n",
    "from keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In this Notebook, we will Implement Variational Autoencoder on MNIST data set\n",
    "\n",
    "### First step will load the data and we use keras datasets to do that.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train,y_train),(x_test,y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train.shape\n",
    "x_=np.zeros((60000,784))\n",
    "x_t=np.zeros((10000,784))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### we will Normlize our Image data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(60000):\n",
    "    x_[i] = np.reshape(x_train[i],(784))/255.0\n",
    "    if i<10000:\n",
    "        x_t[i] = np.reshape(x_test[i],(784))/255.0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 784)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_t.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f2fc1cbca58>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mFep7f13Yc5foa6EKeN64wg8Iiiv8gKAIPxAU4QeCIvxAUIQfCIrwA0ERfiAowg8E9f/SngG+hKGvjwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x_train[i],cmap = 'Greys')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now we will define our model in Keras\n",
    "### sampling layer will randomly sample mean layer and standered diviation layer "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampling(args):\n",
    "    z_mean, z_std = args\n",
    "    batch = K.shape(z_mean)[0]\n",
    "    dim = K.int_shape(z_mean)[1]\n",
    "    # by default, random_normal has mean=0 and std=1.0\n",
    "    epsilon = K.random_normal(shape=(batch, dim))\n",
    "    return z_mean + K.exp(0.5 * z_std) * epsilon\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "inpu =  Input(shape = (784,))\n",
    "# encoder \n",
    "h1 = Dense(256,activation = 'relu')(inpu)\n",
    "z_mean = Dense(2,activation = 'linear')(h1)\n",
    "z_std = Dense(2,activation = 'linear')(h1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sampling layer  \n",
    "z = Lambda(sampling, output_shape=(2,), name='z')([z_mean, z_std])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            (None, 784)          0                                            \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 256)          200960      input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_3 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 201,988\n",
      "Trainable params: 201,988\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "enco = Model(inpu,[z_mean,z_std])\n",
    "enco.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# decoder model\n",
    "x = Dense(256, activation='relu')(z)\n",
    "out = Dense(784, activation='sigmoid')(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We can see our model by using keras model function Model.summary() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            (None, 784)          0                                            \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 256)          200960      input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_3 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "z (Lambda)                      (None, 2)            0           dense_2[0][0]                    \n",
      "                                                                 dense_3[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_4 (Dense)                 (None, 256)          768         z[0][0]                          \n",
      "__________________________________________________________________________________________________\n",
      "dense_5 (Dense)                 (None, 784)          201488      dense_4[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 404,244\n",
      "Trainable params: 404,244\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "\n",
    "vae = Model(inpu,out)\n",
    "vae.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now we will define our loss for VAE \n",
    "#### VAE loss = reconstruction_error + KL divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_(y_true,y_pred):\n",
    "    recon = mse(y_true,y_pred)*784\n",
    "    kl = 0.5 * K.sum(K.exp(z_std) + K.square(z_mean) - 1. - z_std, axis=1)\n",
    "    return K.mean(recon + kl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            (None, 784)          0                                            \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 256)          200960      input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_2 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_3 (Dense)                 (None, 2)            514         dense_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "z (Lambda)                      (None, 2)            0           dense_2[0][0]                    \n",
      "                                                                 dense_3[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "dense_4 (Dense)                 (None, 256)          768         z[0][0]                          \n",
      "__________________________________________________________________________________________________\n",
      "dense_5 (Dense)                 (None, 784)          201488      dense_4[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 404,244\n",
      "Trainable params: 404,244\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "vae.compile(optimizer='adam',loss = loss_)\n",
    "vae.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 12s 200us/step - loss: 52.7601\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 11s 191us/step - loss: 42.7638\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 12s 196us/step - loss: 41.8870\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 12s 198us/step - loss: 41.3325\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 12s 196us/step - loss: 40.9732\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 12s 202us/step - loss: 40.6260\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 12s 207us/step - loss: 40.3371\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 12s 207us/step - loss: 40.1086\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 12s 206us/step - loss: 39.9010\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 12s 204us/step - loss: 39.7104\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f2fc04bc908>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vae.fit(x_,x_,epochs=10,batch_size=64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = vae.predict(x_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 784)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7951331"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(pp[456])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f2fb079a7b8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.reshape(pp[5],(28,28)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f2fc05bea90>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zUDNLqwXeu1aa8bqM8K+VNN3MPmhmJ0n6tKTVJfTxLmY2KvsiRmY2StLH1HqzD6+WtCi7v0jSQyX28ltaZebmvJmlVfJ712ozXpfyI59sKOObktokrXD3f2p6E0Mws2ka2NtLA5OY3lVmb2a2StJ8DZz1tVvSDZIelPQjSWdI2iHpU+7e9C/ecnqbr4GPru/M3Hz0GLvJvV0o6QlJGyT1Z4uv18DxdWnvXaKvhSrhfeMXfkBQ/MIPCIrwA0ERfiAowg8ERfiBoAg/EBThB4Ii/EBQ/w91XUG8jwQcSAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x_train[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}