convolution-digit-recognizer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Acknowledgement\n",
    "\n",
    "Code taken from [fastai: lesson 0](http://course.fast.ai/lessons/lesson0.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Preparations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math,sys,os,numpy as np\n",
    "from numpy.linalg import norm\n",
    "from PIL import Image\n",
    "from matplotlib import pyplot as plt, rcParams, rc\n",
    "from scipy.ndimage import imread\n",
    "from skimage.measure import block_reduce\n",
    "from scipy.ndimage.filters import correlate, convolve\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "from ipywidgets.widgets import *\n",
    "rc('animation', html='html5')\n",
    "rcParams['figure.figsize'] = 3, 6\n",
    "%precision 4\n",
    "np.set_printoptions(precision=4, linewidth=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "from torchvision import models,transforms,datasets\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Download MNIST data on disk and convert it to pytorch compatible formating.\n",
    "\n",
    "```torchvision.datasets``` features support (download, formatting) for a collection of popular datasets. The list of available datasets in ```torchvision``` can be found [here](http://pytorch.org/docs/master/torchvision/datasets.html).\n",
    "\n",
    "Note that the download is performed only once. The function will always check first if the data is already on disk.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torchvision.datasets.mnist.MNIST at 0x7ffa81555ef0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "root_dir = '/home/lelarge/courses/data/MNIST/'\n",
    "torchvision.datasets.MNIST(root=root_dir,download=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST datasets consists of small images of hand-written digits. The images are grayscale and have size 28 x 28. There are 60,000 training images and 10,000 testing images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_set = torchvision.datasets.MNIST(root=root_dir, train=True, download=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define and initialize a data loader for the MNIST data already downloaded on disk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "MNIST_dataset = torch.utils.data.DataLoader(train_set, batch_size=1, shuffle=True, num_workers=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the current notebook, since we are doing no training, we can format data as _numpy ndarrays_ which are easier to plot in matplotlib. The same operations can be easily performed on _pytorch Tensors_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = train_set.train_data.numpy().astype(np.float32)/255\n",
    "b = train_set.train_labels.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28) (60000,)\n"
     ]
    }
   ],
   "source": [
    "print(a.shape,b.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Save data as compressed ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.savez_compressed(os.path.join(root_dir, 'train'), images=a, labels=b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Data visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience we define a few functions for formatting and plotting our image data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# plot multiple images\n",
    "def plots(ims, interp=False, titles=None):\n",
    "    ims=np.array(ims)\n",
    "    mn,mx=ims.min(),ims.max()\n",
    "    f = plt.figure(figsize=(12,24))\n",
    "    for i in range(len(ims)):\n",
    "        sp=f.add_subplot(1, len(ims), i+1)\n",
    "        if not titles is None: sp.set_title(titles[i], fontsize=18)\n",
    "        plt.imshow(ims[i], interpolation=None if interp else 'none', vmin=mn,vmax=mx)\n",
    "\n",
    "# plot a single image\n",
    "def plot(im, interp=False):\n",
    "    f = plt.figure(figsize=(3,6), frameon=True)\n",
    "    plt.imshow(im, interpolation=None if interp else 'none')\n",
    "\n",
    "plt.gray()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.load(os.path.join(root_dir, 'train.npz'))\n",
    "images=data['images']\n",
    "labels=data['labels']\n",
    "n=len(images)\n",
    "images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa814ea940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(images[5000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[5000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa81476f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(images[5000:5005], titles=labels[5000:5005])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Filters and convolutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a simple 3x3 filter, ie a 3x3 matrix (see [Sobel operator](https://en.wikipedia.org/wiki/Sobel_operator) for more examples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAADKCAYAAADHPo59AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72bba2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "top=[[-1,-1,-1],\n",
    "     [ 1, 1, 1],\n",
    "     [ 0, 0, 0]]\n",
    "\n",
    "plot(top)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In some fields, convolution or filtering can be better understood as _correlations_. \n",
    "In practice we slide the filter matrix over the image (a bigger matrix) always selecting patches from the image with the same size as the filter. We compute the dot product between the filter and the image patch and store the scalar response which reflects the degree of similarity/correlation between the filter and image patch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "corrtop = correlate(images[5000], top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "?correlate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIjRAEKEBgggNEERogCBCAwQRGiDov3iZowuIxqUGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa732e3f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(corrtop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By rotating the filter with 90 degrees and calling the ```convolve``` function we get the same response as with the previously called ```correlate``` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1,  1,  0],\n",
       "       [-1,  1,  0],\n",
       "       [-1,  1,  0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.rot90(top, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIjRAEKEBgggNEERogCBCAwQRGiDov3iZowuIxqUGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72b63c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "convtop = convolve(images[5000], np.rot90(top,2))\n",
    "plot(convtop)\n",
    "np.allclose(convtop, corrtop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate a few more variants of our simple 3x3 filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAC0CAYAAACEyqqiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngAkUZwAAmEBxBgCACf4NIdf5/MfjwlcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72fd8160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "straights=[np.rot90(top,i) for i in range(4)]\n",
    "plots(straights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We proceed similarly to generate a set of filters with a different behavior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h72yu0R/DJqx/tNyu1rX2v7c5Rl9/sjmPYZFP1aiq65J8JcmfXPxDkCTd/XJ3b69un0hy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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa7323e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "br=[[ 0, 0, 1],\n",
    "    [ 0, 1,-1.5],\n",
    "    [ 1,-1.5, 0]]\n",
    "\n",
    "diags = [np.rot90(br,i) for i in range(4)]\n",
    "plots(diags)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compose filters to obtain more complex patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jxU1M29Feu1dccQWA/LK17OM8SNFcE+G5z2sU0J47tc/wxRdfDKD/ormmoIWF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72f785f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rots = straights + diags\n",
    "corrs = [correlate(images[5000], rot) for rot in rots]\n",
    "plots(corrs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we illustrate the effect of downsampling.\n",
    "We select the most basic downsampling technique: __max pooling__. We keep only the maximum value for sliding windows of size ```7x7```.\n",
    "__Max pooling__ is a handy technique with a few useful perks:\n",
    "- since it selects the maximum values it ensures invariance to translations\n",
    "- reducing the size is helpful since data becomes more compact and easier to compare\n",
    "- we will see later in this course that since max pooling reduces the size of our images, the operations performed later on in the network have bigger receptive field / concern a bigger patch in the input image and allow the discovery of higher level patterns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAABqCAYAAABeQoJYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACArP0PuMlGRP1dC7cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72d797b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def pool(im): return block_reduce(im, (7,7), np.max)\n",
    "\n",
    "plots([pool(im) for im in corrs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. A simple classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we will construct a basic classifier similar to k-nearest neighbors.\n",
    "Our classifier will tell us whether a given image depicts a _one_ or an _eight_.\n",
    "\n",
    "To this end we select a set of training images depicting _eights_ and _ones_, we convolve them with our set of filters, pool them and average them for each class and filter. We will thus obtain a set of _representative_ signatures for _eights_ and for _ones_. \n",
    "Given a new test image we compute its features by convolution and pooling with the same filters and then compare them with the _representative_ features. The class with the most _similar_ features is chosen as prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fetch all images from the _eight_ class and from the _one_ class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eights=[images[i] for i in range(n) if labels[i]==8]\n",
    "ones=[images[i] for i in range(n) if labels[i]==1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5851, 6742)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(eights), len(ones)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GAQAA4C3veoabN2+u8u23367yDTfcENjH7fl96623VH7nnXdCj3nGGWdkPE4UltvX6fZ0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\ndgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72b85a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa733be668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(eights[:5])\n",
    "plots(ones[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We keep 1000 images of _eight_ for the test set and use the remaining ones for the training: we convolve them with our bank of filters, perform max pooling on the responses and store them in ```pool8```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pool8 = [np.array([pool(correlate(im, rot)) for im in eights[1000:]]) for rot in rots]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, (4851, 4, 4))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pool8), pool8[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the result of the first filter+pooling on the first 5 _eights_ in our set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAACWCAYAAAA8Els6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ8MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa733671d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(pool8[0][0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We normalize the data in order to smoothen activations and bring them to similar ranges of values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalize(arr): return (arr-arr.mean())/arr.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we compute the average _eight_ by averaging all responses for each filter from _rots_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filts8 = np.array([ims.mean(axis=0) for ims in pool8])\n",
    "filts8 = normalize(filts8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should obtain a set of canonical _eights_ responses for each filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAABqCAYAAABeQoJYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nN28AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa72ea37b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(filts8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We proceed similarly with 1000 training sample from the _one_ class and plot the canonical _ones_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pool1 = [np.array([pool(correlate(im, rot)) for im in ones[1000:]]) for rot in rots]\n",
    "filts1 = np.array([ims.mean(axis=0) for ims in pool1])\n",
    "filts1 = normalize(filts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAABqCAYAAABeQoJYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa731e02b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(filts1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do you notice any differences between ```filts8``` and ```filts1```? Which ones?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a function that correlates a given image with all filters from ```rots``` and max pools the responses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pool_corr(im): return np.array([pool(correlate(im, rot)) for rot in rots])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAABqCAYAAABeQoJYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAACqpJREFUeJzt3U9oVXcaxvHnTbymosWFozhomMyoXYht6ZAWpODCWejU\nQlcBZ6S40a4KCrPpyq0UdLqSgjBDQyiU0VachVIG1MUI9s9IB43SIROptlawKZpWbeo17yzMFNuZ\nNuee8/7uOf7y/cCFJCRP3vPkYN4cjveauwsAAADIVU/dAwAAAAApsfACAAAgayy8AAAAyBoLLwAA\nALLGwgsAAICssfACAAAgayy8AAAAyBoLLwAAALLGwgsAAICssfACAAAga/NShJpZo16veM2aNSE5\nPT3V/z64du2abty4YZ1+XVSnjzzySESMVq5cGZIzPj5eOWN6elru3nGnUvPO1SgR52rZXpvW6cKF\nC0NyIv4duXz5siYmJh76TqMsWbIkJGdiYuILd1/a6ddF9bp48eKIGM2bF/Mr+d69e5Uzbt++ramp\nqdrO1UWLFkXEhJ1jX3/9dUhO3edqX19fREzYLjE5OVk5w90L/a5KsvA2zYEDB0JyFixYUDljx44d\nAZOUt3r16pCcV199NSRnaGiocsY333wTMEleIpa8W7duBUxSv8cffzwk59ixY5UzNm7cGDBJPp5/\n/vmQnOHh4U9CgkrasGFDSE7Ucnbz5s3KGSdPngyYpLzBwcGQnG3btoXknD59OiTnjTfeqPVc7e/v\nD8lZu3ZtSM7x48crZ7Tb7UKfxy0NAAAAyBoLLwAAALLGwgsAAICsFVp4zWyzmX1sZmNm9krqoeYC\nOk2DXuPRaRr0Go9O06DXeHTafbMuvGbWK+mApN9KWivpd2YWc7fyHEWnadBrPDpNg17j0Wka9BqP\nTutR5ArvM5LG3H3c3b+V9JakF9KOlT06TYNe49FpGvQaj07ToNd4dFqDIgvvCklXHnj/05mPfY+Z\nvWRmH5rZh1HDZYxO06DXeHSaxqy90mnHOFfT4FyNx7lag7Dn4XX3g5IOSvk+SXq30Wka9BqPTuPR\naRr0Go9O06DXWEWu8H4m6cFnKl458zGUR6dp0Gs8Ok2DXuPRaRr0Go9Oa1Bk4f1A0hoz+6WZzZe0\nVdJf046VPTpNg17j0Wka9BqPTtOg13h0WoNZb2lw97aZvSzpXUm9kv7s7qPJJ8sYnaZBr/HoNA16\njUenadBrPDqtR6F7eN39mKTqLySP79BpGvQaj07ToNd4dJoGvcaj0+7jldYAAACQNRZeAAAAZI2F\nFwAAAFkLex7eFMbGxkJyVq1aFZLT29tbOWN6ejpgkvJee+21kJxTp06F5Ny+fTskp2579uwJydm1\na1dIzpYtWypnnDt3LmCS8oaHh0NynnjiiZCc8+fPV864c+dOwCTljYyMhOS0Wq2QnCtXrsz+SQ+B\n7du3h+S8//77ITntdrtyRk9PvdfDNm/eHJLz9NNPh+Ts3LkzJKduQ0NDITlPPvlkSM74+HjljKK7\nIld4AQAAkDUWXgAAAGSNhRcAAABZY+EFAABA1lh4AQAAkDUWXgAAAGSNhRcAAABZY+EFAABA1lh4\nAQAAkDUWXgAAAGSNhRcAAABZY+EFAABA1lh4AQAAkDUWXgAAAGSNhRcAAABZY+EFAABA1lh4AQAA\nkLV5KUJbrZaWL19eOWf//v0B00gnTpwIyZmeng7JqdOtW7dCcnLoItKqVatCcvbt2xeSc+bMmZCc\nOm3atCkkp6cn5u/6ZcuWheTUaWBgICSn3W6H5GzdujUkp6xWq6WlS5dWzjly5EjANNLU1FRIzuHD\nh0NyyojqdP369QHTSLt37w7JqdvChQu1bt26yjmTk5MB00gjIyMhOefPnw/JKYIrvAAAAMgaCy8A\nAACyxsILAACArLHwAgAAIGuzLrxm1m9mJ83sgpmNmtmubgyWMzpNg17j0Wka9BqPTtOg13h0Wo8i\nz9LQlvQHdz9rZo9K+oeZ/c3dLySeLWd0mga9xqPTNOg1Hp2mQa/x6LQGs17hdffP3f3szNtfSboo\naUXqwXJGp2nQazw6TYNe49FpGvQaj07r0dE9vGY2IOkpSe+lGGYuotM06DUenaZBr/HoNA16jUen\n3VP4hSfMbJGktyXtdvf/eeZiM3tJ0kuS1NvbGzZgzjrpFMXRazw6TeOneqXTcvhdlUbRc5VOi+vk\nXJ0/f36Xp8tPoSu8ZtbS/R/Km+7+zv/7HHc/6O6D7j4Y9cpGOeu00+5O9/Ci13h0msZsvdJp5/hd\nlUYn5yqdFtPpudpqtbo7YIaKPEuDSfqTpIvu/sf0I+WPTtOg13h0mga9xqPTNOg1Hp3Wo8ifYs9K\nelHSRjP7aObxXOK5ckenadBrPDpNg17j0Wka9BqPTmsw6z287v53SdaFWeYMOk2DXuPRaRr0Go9O\n06DXeHRaD262AQAAQNZYeAEAAJA1Fl4AAABkjYUXAAAAWSv8whOdaLfbun79euWcdevWBUwjvf76\n6yE5OXD3kJy9e/eG5NStr69PAwMDlXM2bdpUfRhJly9fDsnJwaFDh0JyIv4tqltfX5/6+/sr50R1\ncenSpZCcut29e1dXr16tnDM4GPNUyUePHg3JqVNfX58ee+yxyjntdjtgGunUqVMhOXUzMy1YsKBy\nzooVMa9gPDo6GpLTTVzhBQAAQNZYeAEAAJA1Fl4AAABkjYUXAAAAWWPhBQAAQNZYeAEAAJA1Fl4A\nAABkjYUXAAAAWWPhBQAAQNZYeAEAAJA1Fl4AAABkjYUXAAAAWWPhBQAAQNZYeAEAAJA1Fl4AAABk\njYUXAAAAWWPhBQAAQNbM3eNDza5L+uQnPuVnkr4I/8bldXOeX7j70k6/qECn0tzttVSnEufqLDhX\n49FpGvQaj07TmCu9Nq7TJAvvrN/U7EN3H+z6N/4RTZunrKYdR9PmKaNpx9C0ecpq2nE0bZ4ymnYM\nTZunrKYdR9PmKaNpx9C0ecpq0nE0aZb/4pYGAAAAZI2FFwAAAFmra+E9WNP3/TFNm6esph1H0+Yp\no2nH0LR5ymracTRtnjKadgxNm6esph1H0+Ypo2nH0LR5ymrScTRpFkk13cMLAAAAdAu3NAAAACBr\nXV94zWyzmX1sZmNm9kq3v/8PZuk3s5NmdsHMRs1sV53zlEWnadBrPDpNg17j0Wka9BqPTgty9649\nJPVK+rekX0maL+mfktZ2c4YfzPNzSb+eeftRSf+qcx46bc6DXun0YXnQK50+LA96pdM6H92+wvuM\npDF3H3f3byW9JemFLs/wHXf/3N3Pzrz9laSLklbUNU9JdJoGvcaj0zToNR6dpkGv8ei0oG4vvCsk\nXXng/U/VkCLMbEDSU5Leq3eSjtFpGvQaj07ToNd4dJoGvcaj04L4T2uSzGyRpLcl7Xb3ybrnyQGd\npkGv8eg0DXqNR6dp0Gu8Jnba7YX3M0n9D7y/cuZjtTGzlu7/UN5093fqnKUkOk2DXuPRaRr0Go9O\n06DXeHRaUFefh9fM5un+Dcy/0f0fyAeSfu/uo10b4vvzmKRhSV+6++46ZqiKTtOg13h0mga9xqPT\nNOg1Hp0W19UrvO7elvSypHd1/0bmv9T1Q5nxrKQXJW00s49mHs/VOE/H6DQNeo1Hp2nQazw6TYNe\n49FpcbzSGgAAALLGf1oDAABA1lh4AQAAkDUWXgAAAGSNhRcAAABZY+EFAABA1lh4AQAAkDUWXgAA\nAGSNhRcAAABZ+w8gYBEtCNd3QQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa733bc438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(pool_corr(eights[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sum of squared errors\n",
    "def sse(a,b): return ((a-b)**2).sum()\n",
    "\n",
    "# function used for a voting based classifier that will indicate which one of the \n",
    "# two classes is most likely given the sse distances\n",
    "# n2 comes from norm2\n",
    "# is8_n2 returns 1 if it thinks it's an eight and 0 otherwise\n",
    "def is8_n2(im): return 1 if sse(pool_corr(im),filts1) > sse(pool_corr(im),filts8) else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We perform a check to see if our function actually works. We correlate the an image of _eight_ with ```filts8``` and ```filts1```. It should give smaller error for the _eights_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(103.67323, 126.09805)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sse(pool_corr(eights[0]), filts8), sse(pool_corr(eights[0]), filts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa732a88d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(eights[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now test our classifier on the 1000 images of _eights_ and 1000 images of _ones_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[969, 37]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([is8_n2(im) for im in ims]).sum() for ims in [eights[:1000],ones[:1000]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It said in 969 cases it is an _eight_ and 37 case it is a _one_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now test the opposite, ie it's not an _eight_ , it's not a _one_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[31, 963]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([(1-is8_n2(im)) for im in ims]).sum() for ims in [eights[:1000],ones[:1000]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test the our simple classifier with a new distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sum of absolute differences\n",
    "def n1(a,b): return (np.fabs(a-b)).sum()\n",
    "\n",
    "# is8_n1 returns 1 if it thinks it's an eight and 0 otherwise\n",
    "def is8_n1(im): return 1 if n1(pool_corr(im),filts1) > n1(pool_corr(im),filts8) else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[941, 31]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([is8_n1(im) for im in ims]).sum() for ims in [eights[:1000],ones[:1000]]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[59, 969]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([(1-is8_n1(im)) for im in ims]).sum() for ims in [eights[:1000],ones[:1000]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have successfully built a classifier for _eights_ and _ones_ using features extract with a bank of pre-defined features and a set of training samples. We will improved it during the next lectures.\n",
    "\n",
    "#### Questions\n",
    "- What are the advantages of this method?\n",
    "- What are the weak points of this method?\n",
    "- How can we improve it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### A few useful ressources about convolutions:\n",
    "1. [Convolution animations](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md)\n",
    "2. [Interactive image kernels](http://setosa.io/ev/image-kernels/)\n",
    "3. [CS231n: Convolutional Neural Networks](http://cs231n.github.io/convolutional-networks/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## End"
   ]
  }
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