MNIST in Keras.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building a simple neural-network with Keras\n",
    "\n",
    "**Author: Xavier Snelgrove**\n",
    "\n",
    "This is a simple quick-start in performing digit recognition in a neural network in Keras, for a short tutorial at the University of Toronto. It is largely based on the `mnist_mlp.py` example from the Keras source.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Install prerequisites\n",
    "First steps (instructions for Mac or Linux). You need to install a recent version of Python, plus the packages `keras`, `numpy`, `matplotlib` and `jupyter`.\n",
    "\n",
    "### Install a recent Python\n",
    "\n",
    "If you haven't installed a recent Python I recommend installing via Homebrew on a Mac from http://brew.sh and then installing Python via `brew install python`.\n",
    "\n",
    "\n",
    "### Configure a virtual environment\n",
    "\n",
    "You can install the packages globally, but I suggest installing them in a `virtualenv` virtual environment that basically encapsulates a full isolated Python environment. First you'll need to install a Python package manager called `pip` thus:\n",
    "\n",
    "    easy_install pip\n",
    "    \n",
    "(If you get a permissions error, try adding a `sudo` to the beginning, so `sudo easy_install pip`)\n",
    "\n",
    "Now install virtualenv thus:\n",
    "\n",
    "    pip install virtualenv\n",
    "\n",
    "Navigate to your home directory `cd ~` and create a virtual environment. We'll call it `kerasenv`\n",
    "\n",
    "    virtualenv kerasenv\n",
    "\n",
    "Now, to switch your shell environment to be within the env:\n",
    "\n",
    "    source kerasenv/bin/activate\n",
    "    \n",
    "Great: now you can install the other prerequisites into this environment.\n",
    "\n",
    "    pip install numpy jupyter keras matplotlib\n",
    "    \n",
    "\n",
    "## Open a new notebook\n",
    "\n",
    "Now that everything's installed, you can open one of these web-based Python environments with the following command:\n",
    "\n",
    "    ipython notebook\n",
    "    \n",
    "Create a new Python notebook from the \"New\" menu at the top-right:\n",
    "\n",
    "<img src=\"newnotebook.png\">\n",
    "\n",
    "You should now be able to run Python in your browser!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time to build a neural network!\n",
    "First let's import some prerequisites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using Theano backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (7,7) # Make the figures a bit bigger\n",
    "\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Dropout, Activation\n",
    "from keras.utils import np_utils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train original shape (60000, 28, 28)\n",
      "y_train original shape (60000,)\n"
     ]
    }
   ],
   "source": [
    "nb_classes = 10\n",
    "\n",
    "# the data, shuffled and split between tran and test sets\n",
    "(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
    "print(\"X_train original shape\", X_train.shape)\n",
    "print(\"y_train original shape\", y_train.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at some examples of the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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Czknnzp2derXVVnPqpqYmp/7rX/+ae5tK5Z+v4k8k6XvsscdaLCt1jCRreWbEHzM76aST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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11326a668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(9):\n",
    "    plt.subplot(3,3,i+1)\n",
    "    plt.imshow(X_train[i], cmap='gray', interpolation='none')\n",
    "    plt.title(\"Class {}\".format(y_train[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Format the data for training\n",
    "Our neural-network is going to take a single vector for each training example, so we need to reshape the input so that each 28x28 image becomes a single 784 dimensional vector. We'll also scale the inputs to be in the range [0-1] rather than [0-255]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training matrix shape (60000, 784)\n",
      "Testing matrix shape (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "X_train = X_train.reshape(60000, 784)\n",
    "X_test = X_test.reshape(10000, 784)\n",
    "X_train = X_train.astype('float32')\n",
    "X_test = X_test.astype('float32')\n",
    "X_train /= 255\n",
    "X_test /= 255\n",
    "print(\"Training matrix shape\", X_train.shape)\n",
    "print(\"Testing matrix shape\", X_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modify the target matrices to be in the one-hot format, i.e.\n",
    "\n",
    "```\n",
    "0 -> [1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
    "1 -> [0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
    "2 -> [0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
    "etc.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Y_train = np_utils.to_categorical(y_train, nb_classes)\n",
    "Y_test = np_utils.to_categorical(y_test, nb_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Build the neural network\n",
    "Build the neural-network. Here we'll do a simple 3 layer fully connected network.\n",
    "<img src=\"figure.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(512, input_shape=(784,)))\n",
    "model.add(Activation('relu')) # An \"activation\" is just a non-linear function applied to the output\n",
    "                              # of the layer above. Here, with a \"rectified linear unit\",\n",
    "                              # we clamp all values below 0 to 0.\n",
    "                           \n",
    "model.add(Dropout(0.2))   # Dropout helps protect the model from memorizing or \"overfitting\" the training data\n",
    "model.add(Dense(512))\n",
    "model.add(Activation('relu'))\n",
    "model.add(Dropout(0.2))\n",
    "model.add(Dense(10))\n",
    "model.add(Activation('softmax')) # This special \"softmax\" activation among other things,\n",
    "                                 # ensures the output is a valid probaility distribution, that is\n",
    "                                 # that its values are all non-negative and sum to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compile the model\n",
    "Keras is built on top of Theano (and now TensorFlow as well), both packages that allow you to define a *computation graph* in Python, which they then compile and run efficiently on the CPU or GPU without the overhead of the Python interpreter.\n",
    "\n",
    "When compiing a model, Keras asks you to specify your **loss function** and your **optimizer**. The loss function we'll use here is called *categorical crossentropy*, and is a loss function well-suited to comparing two probability distributions.\n",
    "\n",
    "Here our predictions are probability distributions across the ten different digits (e.g. \"we're 80% confident this image is a 3, 10% sure it's an 8, 5% it's a 2, etc.\"), and the target is a probability distribution with 100% for the correct category, and 0 for everything else. The cross-entropy is a measure of how different your predicted distribution is from the target distribution. [More detail at Wikipedia](https://en.wikipedia.org/wiki/Cross_entropy)\n",
    "\n",
    "The optimizer helps determine how quickly the model learns, how resistent it is to getting \"stuck\" or \"blowing up\". We won't discuss this in too much detail, but \"adam\" is often a good choice (developed here at U of T)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.compile(loss='categorical_crossentropy', optimizer='adam')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train the model!\n",
    "This is the fun part: you can feed the training data loaded in earlier into this model and it will learn to classify digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/4\n",
      "60000/60000 [==============================] - 10s - loss: 0.2521 - acc: 0.9245 - val_loss: 0.1131 - val_acc: 0.9651\n",
      "Epoch 2/4\n",
      "60000/60000 [==============================] - 10s - loss: 0.1016 - acc: 0.9687 - val_loss: 0.0827 - val_acc: 0.9746\n",
      "Epoch 3/4\n",
      "60000/60000 [==============================] - 11s - loss: 0.0711 - acc: 0.9779 - val_loss: 0.0668 - val_acc: 0.9791\n",
      "Epoch 4/4\n",
      "60000/60000 [==============================] - 11s - loss: 0.0557 - acc: 0.9816 - val_loss: 0.0642 - val_acc: 0.9805\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x12655bbe0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, Y_train,\n",
    "          batch_size=128, nb_epoch=4,\n",
    "          show_accuracy=True, verbose=1,\n",
    "          validation_data=(X_test, Y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finally, evaluate its performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score: 0.0642029843267\n",
      "Test accuracy: 0.9805\n"
     ]
    }
   ],
   "source": [
    "score = model.evaluate(X_test, Y_test,\n",
    "                       show_accuracy=True, verbose=0)\n",
    "print('Test score:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspecting the output\n",
    "\n",
    "It's always a good idea to inspect the output and make sure everything looks sane. Here we'll look at some examples it gets right, and some examples it gets wrong."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/10000 [==============================] - 0s     \n"
     ]
    }
   ],
   "source": [
    "# The predict_classes function outputs the highest probability class\n",
    "# according to the trained classifier for each input example.\n",
    "predicted_classes = model.predict_classes(X_test)\n",
    "\n",
    "# Check which items we got right / wrong\n",
    "correct_indices = np.nonzero(predicted_classes == y_test)[0]\n",
    "incorrect_indices = np.nonzero(predicted_classes != y_test)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ayVW8l6w1TE5IjkbqDUzxR2heDexoZm/6weNS8pSTTf30cf69jAJ6m9lbZlbs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\nmlwVWBqOciKlKCNS3a0rzOw14D2STe4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cSFtSdUp+U/se4GTn3CLgWmAjYADwFnBlzVoo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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12655b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XTST5sLsXOVe3A48U6F38sSYA44FXvP6Gj282sBCYD7wNnFCw7zrAo/4czQXG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\nehbIA4HJLW0r2i/yiUhDHhE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UU05pcowrr7wy0PGYZjHxmGbXXnttoOPnlOI2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\nGkoiIhKGhpKIiIShoSQiImFoKImISBhvYnwE8Z50LEEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1265ac7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for i, correct in enumerate(correct_indices[:9]):\n",
    "    plt.subplot(3,3,i+1)\n",
    "    plt.imshow(X_test[correct].reshape(28,28), cmap='gray', interpolation='none')\n",
    "    plt.title(\"Predicted {}, Class {}\".format(predicted_classes[correct], y_test[correct]))\n",
    "    \n",
    "plt.figure()\n",
    "for i, incorrect in enumerate(incorrect_indices[:9]):\n",
    "    plt.subplot(3,3,i+1)\n",
    "    plt.imshow(X_test[incorrect].reshape(28,28), cmap='gray', interpolation='none')\n",
    "    plt.title(\"Predicted {}, Class {}\".format(predicted_classes[incorrect], y_test[incorrect]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# That's all!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are lots of other great examples at the Keras homepage at http://keras.io and in the source code at https://github.com/fchollet/keras"
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}