4-NNs-and-images.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Images classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading MNIST, dataset with hand-written numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torchvision import datasets, transforms\n",
    "from torch.autograd import Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
      "Processing...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "# download data, transform it (to tensor and normalize images)\n",
    "# the result is iterator over batches \n",
    "batch_size = 64\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./data', train=True, download=True,\n",
    "                   transform=transforms.Compose([\n",
    "                       transforms.ToTensor(),\n",
    "                       transforms.Normalize((0.1307,), (0.3081,))\n",
    "                   ])),\n",
    "    batch_size=batch_size, shuffle=True)\n",
    "\n",
    "test_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./data', train=False, transform=transforms.Compose([\n",
    "                       transforms.ToTensor(),\n",
    "                       transforms.Normalize((0.1307,), (0.3081,))\n",
    "                   ])),\n",
    "    batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(64, 1, 28, 28)\n"
     ]
    },
    {
     "data": {
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kcjm1tbW88MILHD9+nOzsbOx2O52dnZw7d47l5WXC4TBarZbnn3+enJycWDd5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\nERHZQP4/eI+bKSjrW1YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0c67234290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for (data, target) in train_loader:\n",
    "    samples = data.numpy()\n",
    "    print samples.shape\n",
    "    for i in range(25):\n",
    "        plt.subplot(5, 5, i + 1)\n",
    "        plt.imshow(samples[i, 0, :, :], cmap='gray')\n",
    "        plt.axis('off')\n",
    "    break # only for a first batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define NN configuration\n",
    "\n",
    "- convolution layer, max pooling, activation\n",
    "- convolution layer, dropout, max pooling, activation\n",
    "- flattening\n",
    "- dense layer, activation, dropout\n",
    "- dense layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from torch.nn import Sequential, Conv2d, Dropout2d, Linear, MaxPool2d, Softmax, ReLU\n",
    "from torch.optim import SGD, Adagrad, Adadelta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define flattening layer\n",
    "class Flatten(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Flatten, self).__init__()\n",
    "        \n",
    "    def forward(self, x):\n",
    "        return x.view(len(x), -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define NN configuration\n",
    "model = Sequential(\n",
    "    Conv2d(1, 10, kernel_size=5), # one image, apply 10 filters, each filter is a matrix 5x5 -> 10 images with size 24x24\n",
    "    MaxPool2d(kernel_size=2), # maxpool operation, compress each of 10 images twice -> images with size 12X12\n",
    "    ReLU(), # add non linear activation\n",
    "    Conv2d(10, 20, kernel_size=5), # 10 images, apply 20 filters, each filter is a matrix 5x5 -> 20 images with size 8x8\n",
    "    Dropout2d(p=0.5), # deactivate neuron with probability 0.5 during training\n",
    "    MaxPool2d(kernel_size=2), # maxpool operation, compress each of 20 images twice -> 20 images with size 4X4\n",
    "    ReLU(), # add non linear activation\n",
    "    Flatten(), # 20 images with size 4x4 = 320 values\n",
    "    Linear(320, 50), # add dense layer\n",
    "    ReLU(), # add non linear activation\n",
    "    Dropout2d(p=0.5), # deactivate neuron with probability 0.5 during training\n",
    "    Linear(50, 10), # dense layer, output is equal to number of classes\n",
    ")\n",
    "\n",
    "# define optimizer\n",
    "optimizer = SGD(model.parameters(), lr=0.01, momentum=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from torch.nn import CrossEntropyLoss\n",
    "\n",
    "def train(epoch, train_loader, model, optimizer, log_interval=100):\n",
    "    # define loss function\n",
    "    loss_function = CrossEntropyLoss()\n",
    "    # set training mode for correctness of Dropout layer\n",
    "    model.train()\n",
    "    # iterate over batches\n",
    "    for batch_idx, (data, target) in enumerate(train_loader):\n",
    "        data, target = Variable(data), Variable(target)\n",
    "        # set gradient to zero\n",
    "        optimizer.zero_grad()\n",
    "        # compute output of NN\n",
    "        output = model(data)\n",
    "        # compute loss function (logistic loss)\n",
    "        loss = loss_function(output, target)\n",
    "        # propagate gradients\n",
    "        loss.backward()\n",
    "        # make optimization step\n",
    "        optimizer.step()\n",
    "        if batch_idx % log_interval == 0:\n",
    "            print('Train Epoch: {} [{}/{} ({:.0f}%)]\\tLoss: {:.6f}'.format(\n",
    "                epoch, batch_idx * len(data), len(train_loader.dataset),\n",
    "                100. * batch_idx / len(train_loader), loss.data[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from torch.nn.functional import softmax\n",
    "\n",
    "\n",
    "def test(epoch, train_loader, model, optimizer):\n",
    "    # set evaluation mode for correctness of Dropout layer\n",
    "    model.eval()\n",
    "    \n",
    "    test_loss = 0\n",
    "    correct = 0\n",
    "    \n",
    "    loss_function = CrossEntropyLoss()\n",
    "    \n",
    "    # iterate over test samples\n",
    "    for data, target in test_loader:\n",
    "        data, target = Variable(data, volatile=True), Variable(target)\n",
    "        output = model(data)\n",
    "        test_loss += loss_function(output, target).data[0]\n",
    "        # compute probabilities for each class\n",
    "        proba = softmax(output).data.numpy() \n",
    "        # compute class answers\n",
    "        target_predicted = proba.argmax(axis=1)\n",
    "        correct += numpy.sum(target_predicted == target.data.numpy())\n",
    "\n",
    "    test_loss = test_loss\n",
    "    test_loss /= len(test_loader) # loss function already averages over batch size\n",
    "    print('\\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.3f}%)\\n'.format(\n",
    "        test_loss, correct, len(test_loader.dataset),\n",
    "        100. * correct / len(test_loader.dataset)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train/test the NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Epoch: 1 [0/60000 (0%)]\tLoss: 2.330248\n",
      "Train Epoch: 1 [6400/60000 (11%)]\tLoss: 0.977603\n",
      "Train Epoch: 1 [12800/60000 (21%)]\tLoss: 0.839784\n",
      "Train Epoch: 1 [19200/60000 (32%)]\tLoss: 0.566482\n",
      "Train Epoch: 1 [25600/60000 (43%)]\tLoss: 0.377513\n",
      "Train Epoch: 1 [32000/60000 (53%)]\tLoss: 0.484473\n",
      "Train Epoch: 1 [38400/60000 (64%)]\tLoss: 0.349985\n",
      "Train Epoch: 1 [44800/60000 (75%)]\tLoss: 0.263893\n",
      "Train Epoch: 1 [51200/60000 (85%)]\tLoss: 0.259025\n",
      "Train Epoch: 1 [57600/60000 (96%)]\tLoss: 0.376070\n",
      "\n",
      "Test set: Average loss: 0.1055, Accuracy: 9668/10000 (96.680%)\n",
      "\n",
      "Train Epoch: 2 [0/60000 (0%)]\tLoss: 0.300064\n",
      "Train Epoch: 2 [6400/60000 (11%)]\tLoss: 0.142655\n",
      "Train Epoch: 2 [12800/60000 (21%)]\tLoss: 0.324350\n",
      "Train Epoch: 2 [19200/60000 (32%)]\tLoss: 0.273088\n",
      "Train Epoch: 2 [25600/60000 (43%)]\tLoss: 0.333883\n",
      "Train Epoch: 2 [32000/60000 (53%)]\tLoss: 0.077410\n",
      "Train Epoch: 2 [38400/60000 (64%)]\tLoss: 0.273606\n",
      "Train Epoch: 2 [44800/60000 (75%)]\tLoss: 0.201035\n",
      "Train Epoch: 2 [51200/60000 (85%)]\tLoss: 0.134366\n",
      "Train Epoch: 2 [57600/60000 (96%)]\tLoss: 0.238038\n",
      "\n",
      "Test set: Average loss: 0.0716, Accuracy: 9776/10000 (97.760%)\n",
      "\n",
      "Train Epoch: 3 [0/60000 (0%)]\tLoss: 0.247226\n",
      "Train Epoch: 3 [6400/60000 (11%)]\tLoss: 0.148723\n",
      "Train Epoch: 3 [12800/60000 (21%)]\tLoss: 0.287345\n",
      "Train Epoch: 3 [19200/60000 (32%)]\tLoss: 0.211982\n",
      "Train Epoch: 3 [25600/60000 (43%)]\tLoss: 0.189445\n",
      "Train Epoch: 3 [32000/60000 (53%)]\tLoss: 0.221659\n",
      "Train Epoch: 3 [38400/60000 (64%)]\tLoss: 0.327232\n",
      "Train Epoch: 3 [44800/60000 (75%)]\tLoss: 0.207876\n",
      "Train Epoch: 3 [51200/60000 (85%)]\tLoss: 0.304394\n",
      "Train Epoch: 3 [57600/60000 (96%)]\tLoss: 0.174881\n",
      "\n",
      "Test set: Average loss: 0.0680, Accuracy: 9764/10000 (97.640%)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "epochs = 3\n",
    "\n",
    "for epoch in range(1, epochs + 1):\n",
    "    train(epoch, train_loader, model, optimizer)\n",
    "    test(epoch, train_loader, model, optimizer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Optional exercises\n",
    "\n",
    "1. fine-tune the network above and look at misclassified images. For tuning, you can use the [this approach](http://i.imgur.com/bSiNEq6.gif)\n",
    "\n",
    "2. compare two optimizers: `SGD` (simple stochastic SGD) and `Adadelta` (AdaDelta) on this dataset and study their performance depending on the number of hidden layers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Want to play with more complicated example?\n",
    "\n",
    "Recognize letters from different fonts from notMNIST dataset. Download data from [here](http://yaroslavvb.com/upload/notMNIST/)\n",
    "\n",
    "To load dataset from `.mat` format use `loadmat` function:\n",
    "```\n",
    "    from scipy.io import loadmat\n",
    "    data = loadmat('notMNIST_small.mat')\n",
    "    # plot the first image\n",
    "    plt.imshow(data['images'][:, :, 0], cmap='gray')\n",
    "```\n",
    "\n",
    "To load image from `.png` use the following code:\n",
    "```\n",
    "    from scipy.misc import imread\n",
    "    img = imread('file.png')\n",
    "    # plot the image\n",
    "    plt.imshow(img, cmap='gray')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "- [pytorch documentation](http://pytorch.org/tutorials/)\n",
    "- [keras](https://keras.io) is another popular high-level interface for neural networks\n",
    "- neural networks [playground](http://playground.tensorflow.org)"
   ]
  }
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