Learning To See [Part 4 - Machine Learning].ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 align = 'center'> Learning To See</h1>\n",
    "\n",
    "<h2 align = 'center'> Part 4: Machine Learning </h2>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import finger dataset\n",
    "\n",
    "This dataset has been preprocessed. See Data Preprocessing notebook for more details. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from supportFunctions import *\n",
    "import cPickle as pickle\n",
    "\n",
    "pickleFileName = 'data/fingerDataSet' + '.pickle'\n",
    "pickleFile = open(pickleFileName, 'rb')\n",
    "data = pickle.load(pickleFile)\n",
    "pickleFile.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Our overall dataset has 54, examples, let's just look at 3:\n",
    "exampleIndices = [7, 30, 46]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correct Finger Labels from Leap Motion Software"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jtq3WT9b1sq7Rk08+GcksstFYam0vE3Wnhm7f+9//fnz841GODQAc8BJCCCETEZeTKZCY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\nVKMBrxBCCCGEmGr+H4J9Cuc5QX2rAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d7a1190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(0, (12, 6))\n",
    "\n",
    "for i in range(3):\n",
    "    fig.add_subplot(1,3,i+1)\n",
    "    imageDict = data[exampleIndices[i]]\n",
    "    \n",
    "    X1, y1 = extractFeatures(imageDict, whichImage = 'image1bit', dist = 4)    \n",
    "    yImage = y1.reshape(imageDict['boxHeight'], imageDict['boxWidth'])\n",
    "    \n",
    "    im = makeGrayScale(imageDict)\n",
    "    \n",
    "    #Paint with matches:\n",
    "    im[:,:,0][yImage==1] = 0\n",
    "    im[:,:,1][yImage==1] = .5\n",
    "    im[:,:,2][yImage==1] = 1\n",
    "    \n",
    "    imshow(im, interpolation = 'none')\n",
    "    title('Number of finger pixels = ' + str(sum(y1==1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7867 495\n"
     ]
    }
   ],
   "source": [
    "examples = [data[index] for index in exampleIndices]\n",
    "X, y = extractExamplesFromList(examples, whichImage = 'image1bit', dist = 4)\n",
    "\n",
    "print len(y), sum(y==1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7372"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "7867-495"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From our 3 images, we have 7876 pixels, and of these, 495 correspond to fingers.\n",
    "- Remember we're sampling a 9x9 grid (\"example\") around each pixel, and using this information alone to determine if the pixel belongs to a finger.\n",
    "\n",
    "# Let's have a closer look at our examples\n",
    "\n",
    "- We have 7867 examples, but many are redundant, let's look at just the most common"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Make red and blue colormaps:\n",
    "import matplotlib.colors as mcolors\n",
    "c = mcolors.ColorConverter().to_rgb\n",
    "bw = make_colormap([(1,1,1), (1,1,1), 0.33, c('blue'), c('blue'), 0.66, c('blue')])\n",
    "rw = make_colormap([(1,1,1), (1,1,1), 0.33, c('red'), c('red'), 0.66, c('red')])\n",
    "rwb = make_colormap([c('red'), c('red'), 0.33, (1,1,1), (1,1,1), 0.66, c('blue')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "uniqueExamples, uniqueIndices, uniqueCounts = findUniqueRowsAndCount(X)\n",
    "uniqueLabels = y[uniqueIndices]\n",
    "\n",
    "sI = argsort(uniqueCounts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11058d390>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAEMCAYAAAACksCzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAC81JREFUeJzt3XvMZVV9xvHvwwzFYi1FimCLgHijVaAmpqZNRdN6oaVX\nbSMKdIgJxqQJrRWi9KK1Fou9oE2MiVWpF5RLI9VYrVKVkbZKY0oJioVymRIU0UEuIsNMq6z+sfbI\nZve8531LZt7Xc37fT7Lz5uyzzlr7nH2evfba+81Zaa0hafnts9EbIGl9GHapCMMuFWHYpSIMu1SE\nYZeKKBv2JM9P8qkkX02yM8mtSS5O8mOTcj+X5P1Jbk6yI8mNSd6W5OBJudcleWCFZcekbJKcnWRb\nkvuTXJ3khevxvlVXqt5nT3IS8HTgX4HtwOHA2cBhwDGttVuHcpcABwAXAzcATwL+GNgJHNta2zGU\n+5HhtWOPBD4BfLC19pJR2+cAvwv8HnAVcBLwcuDE1trH98b7lWituQwL8GTgAeCVo3UHzSj3rKHc\naavUdyrwHeCE0bqD6QeK107KfhK4eqM/gz34WX7fRm+Dy0OXsqfxK7hz+Pvt3Staa9+YUe7zw98f\nXaW+LcDXgMtG604A9gXePyl7AXBMkiPmVZhkc5I/GYYAu4a/b0iyeVJu/yTnDsOOncNw5W/Hw48k\nRyZ532goc1OSN4+e35rk0zO24b+SnD96vGUYrjwrySVJ7gKuHJ57xtDurcMw6Lok5yR5xKTOrUn+\naRg2/VuS+5J8Icmvzmj/uCR/l+SOUZ2vnpR5YZLPDfXcNWzX4yZlXprkqiT3JrknyTVJTp/3+S+y\nzasXWW5J9gE2AUcC5wK3AReu8rLnDH+/NKfew4Zy57XWHhg99ePArtbaTZOXXAtkeP6WOW2/F/h1\n4BzgX4CfBv4AeDxwytD2vvQzhWOAP6UPVQ4AXgAcCGxPciT9oPWt4fU30ocyzx+1tdIYb6X1F9A/\nuxfx4HfrCOAa4D3APcBTgdcO2/vSSZ1PAN4CvBH4BnAmcEmSo1trNw/v7SeBy+lDqt8GvkIfWh27\nu6IkrwDeBrwLeD3wqOHv1iTHttbuS/IzwPuG9s6kX786GvihFd7b4tvoU4uNXuhf+AeG5XrgKauU\n/wHgOuALwD5zyp1NP4V/2mT924HbZpR/wrANJ8+p86lDmT+crP/9cVvAy4bHJ86p673AN4FD5pS5\nHPj0jPXbgPNHj7cM2/UXa/i8NwEn08+eDpy0tQs4arTu4KHca0brrqAfDPdbof5HAncD75isP2Ko\n/4zh8auAOzb6+7eei6fxvTd8JvAS+pf/k0kOn1UwySbgIuCxwEntoT321KnAv7fWvrgHt/V4eg84\nawgQ4NnD4+cBt7fWPjqnrucBf99a+9oe2rYGfGi6MsmjkrxpGE7sAv6H3qOG3iOP3dCGHhygtbYd\n+Dr9jIMk308/k7mgtbZrhe34KXpP/oEkm3Yv9DOA6+ifIfSD/IHDMObEJAc8vLe9OMqHvbV2fWvt\n8621i4Hn0nvu10zLJQm9N/xZ4Fdaa9euVOdwqnk08O4ZT9/F7FPFRw9/75zx3LTMVyfrb588fxD9\nyz3PQcCXVynz/zXdLuifwcvpp8vPBZ4B/Nbw3CMmZWe9912jcgfSv7Pz3ttj6AeST9EPLLuX/wae\nRn/ftNauAH6DfgflUvrQ5h+THDOn7oVWfsw+1lq7J8mNwBNnPP12+pfjRa21ratUtYX+5Zo19r8W\n2C/JUeNejH6K3phzHYAHw3Ao/VSa0WPo41yAO4b65rmD1S8w7qT3klOPnrEOJmP5JPsBv0y/8/DW\n0frjVml3JXfRhwvztnv3Z/CbzP4s7/3uxrZ2KXBpkv3p11f+DPgH/u8t1KVQvmcfS3IIvUe+cbL+\nL+nj4NNaax9ZpY59gRcDH2uzr+R/nD4OPXmy/hTgi621eRfnrqD3WifNeG0DPjM8vgw4NMmJc+q6\nDPjF4T2v5BbgyeMr/UmOZ/YBYJb96GP0b0/Wn7bG1z9Ea+1+4J+BU4YDySyfpQf6Sa21q2YsN8yo\nd0dr7WP0A/pjkxz0cLbve13Znj3JpfR/aLmGPlZ/CvA79B75vFG5VwOvpF/ZvSnJM0fVbJ/0zgC/\nRO/53jOr3dba9iTnAWcn+RYP/lPNc4bXrqi1dm2SC4E/Gg4qn+XBq/EfGA0tLgBOBy5Mci79avwP\n0q+0v7m19p/A64CfBz6X5I30A9xhwAtaa6cO9Vw01PM3Sd4NHDV8FnfP287R9n4zyZXAq5LcTj+b\neBn9msfDdSawFbhyOAh/ediun2itndFauzfJWcBbkzyG3lPfQz8beDZweWvtoiSvBw6hXxi8DXgc\ncAb9Osusg/Ti2+grhBu1AGfRL9LcSb/99B/02zWHT8pdTr+yPWs5f0a9H6JfVNo8p+3Q/3tuG3A/\ncDXwa2vc7s30/+DbRh/PbqPfVto0Kbc/8Kbh+Z30ce4lwA+PyjyefrHv68AO+u2sP5/Uczr9LsV9\n9F716cDNwLtGZbYMn8dRM7b3cOCj9MDdDvwV/SDzHeD4yef8mRmvf0hbw7rjgA8P++4++un6WZMy\nJ9DH7XcP+/d64J3A0cPzv0A/EHxl2Ae3AH8NHLrR3829tZT9d1mpGsfsUhGGXSrCsEtFGHapiD13\n6y3xSp+0EVrLWort2fvse+vKfkbvZW+3sTfvTixDG+u5L9ajjUXeF+M21sDTeKkIwy4VYdilIgy7\nVIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCsEtFGHapCMMuFWHYpSIM\nu1SEYZeK2HNzvflT0tLGWONPSduzS0UYdqkIJ4mYtrEskwYsw75YjzYWeV+M21gDe3apCMMuFWHY\npSIMu1SEYZeKMOxSEYZdKsKwS0UYdqkIwy4VYdilIgy7VIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh\n2KUiDLtUhGGXinCSCGnROUmEpDF/N37axrL8jvgy7Iv1aGOR98W4jTWwZ5eKMOxSEYZdKsKwS0UY\ndqkIwy4VYdilIgy7VIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCsEtF\nGHapCMMuFeEkEdKic5IISWNOEjFtY1kmDViGfbEebSzyvhi3sQb27FIRhl0qwrBLRRh2qQjDLhVh\n2KUiDLtUhGGXijDsUhGGXSrCsEtFGHapCMMuFWHYpSIMu1SEYZeKMOxSEYZdKsKwS0UYdqkIwy4V\nYdilIpwkQlp0ThIhacxJIqZtLMukAcuwL9ajjUXeF+M21sCeXSrCsEtFGHapCMMuFWHYpSIMu1SE\nYZeKMOxSEYZdKsKwS0UYdqkIwy4VYdilIgy7VIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUi/N14\nadH5u/GSxgy7VISTREzbWJZJA5ZhX6xHG4u8L8ZtrIE9u1SEYZeKMOxSEYZdKsKwS0UYdqkIwy4V\nYdilIgy7VIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCsEtFOEmEtOic\nJELSmGGXinCSiGkbyzJpwDLsi/VoY5H3xbiNNbBnl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUiDLtU\nhGGXijDsUhGGXSrCsEtFGHapCMMuFWHYpSIMu1SEYZeKMOxSEYZdKsKwS0UYdqkIJ4mQFp2TREga\n83fjp20sy++IL8O+WI82FnlfjNtYA3t2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCsEtFGHapCMMu\nFWHYpSIMu1SEYZeKMOxSEYZdKsKwS0UYdqkIwy4VYdilIgy7VIRhl4ow7FIRThIhLToniZA05iQR\n0zaWZdKAZdgX69HGIu+LcRtrYM8uFWHYpSIMu1SEYZeKMOxSEYZdKsKwS0UYdqkIwy4VYdilIgy7\nVIRhl4ow7FIRhl0qwrBLRRh2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCSSKkRbfGSSL2XNglfU/z\nNF4qwrBLRRh2qQjDLhVh2KUiDLtUhGGXijDsUhGGXSrCsEtFGHapCMMuFWHYpSIMu1SEYZeKMOxS\nEYZdKsKwS0UYdqkIwy4V8b8TPOyhiCj18gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c850990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Show most common example\n",
    "fig = figure(0, (4,4))\n",
    "example = uniqueExamples[0,:].reshape(9,9)\n",
    "p = pcolor(flipud(example), cmap = rw,  linewidth =1.3, \\\n",
    "              color = 'r', vmin = 0, vmax = 1)\n",
    "axis('off')\n",
    "title(str(uniqueCounts[0]) + ' occurances', fontsize = 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now let's look at 40 most common patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fXlUfMntCXIscF1BVX5zkvWOMl82ey03QYJ57WZIvrqqnVtWjk7wgyYNJHjN3WuxJjut5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\n4v8HChtmrqHNf9MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110578390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(0, (16,12))\n",
    "\n",
    "for i in range(40):\n",
    "    index = sI[-1*(i+1)]\n",
    "    example = uniqueExamples[index,:].reshape(9,9)\n",
    "    \n",
    "    if uniqueLabels[index]:\n",
    "        colorMap = bw\n",
    "        mainColor = 'b'\n",
    "    else: \n",
    "        colorMap = rw\n",
    "        mainColor = 'r'\n",
    "    \n",
    "    subplot(6,8,i+1)\n",
    "    p = pcolor(flipud(example), cmap = colorMap,  linewidth =1.3, \\\n",
    "                  color = mainColor, vmin = 0, vmax = 1)\n",
    "    axis('off')\n",
    "    title(str(uniqueCounts[index]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3090 413\n"
     ]
    }
   ],
   "source": [
    "# How many unique examples do we have?\n",
    "fingerExamples, uniqueIndices, uniqueCounts = findUniqueRowsAndCount(X[y==1])\n",
    "print len(uniqueExamples), len(fingerExamples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have 3090 unique examples, 413 of these examples show fingers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's have a closer look at our 413 examples of fingers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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grjw3kW1rZ2DPWq/WrqaDuT/XfX0dzOt3MM/sX43uOa557drzt5q1J7Qmy0zzSgfz/Cwz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\nlLDABAAAoIQFJgAAACX+A7jfgc09C53zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a37e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(0, (16,16))\n",
    "colorMap = bw\n",
    "mainColor = 'b'\n",
    "        \n",
    "for i in range(len(fingerExamples)):\n",
    "    example = fingerExamples[i,:].reshape(9,9)\n",
    "    \n",
    "    subplot(21,21,i+1)\n",
    "    p = pcolor(flipud(example), cmap = colorMap,  linewidth =.4, \\\n",
    "                  color = mainColor, vmin = 0, vmax = 1)\n",
    "    axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Our First Machine Learning Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Here it is, pretty exciting:\n",
    "rules = fingerExamples.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We're simply letting each example of a finger in our dataset be its very own rule. \n",
    "- Now, before we test our algorithm, let's make sure we have a good mean of comparison to our earlier approaches."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's measure the accuracy of our Knowledge Engineering appraoch from part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Here's our confusion Matrix from last time:\n",
    "confusionMatrix = np.array([[48, 447], \\\n",
    "                             [7, 7365]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9422905809075887"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Accuracy = (TP + TN)/(Total Number of Examples)\n",
    "accuracy = (48.+7365.)/(48+7365+447+7)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How is this so high?\n",
    "- It's all about baselines\n",
    "- Let's construct the worlds simplest classifier, all examples are negative. No fingers.\n",
    "- What is our accuracy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9370789373331638"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(7867.-495)/7867"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show and Compute Performance of our First Machine Learning Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+r+48xwde1V3Y7XNf/Fwn9mMf+LFO7HWvf10npqawnD59uhM7e/Zst4FRvnib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\no1d0DgqhlxsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105ef050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(0, (14, 8))\n",
    "showMatches(rules = rules, exampleIndices = exampleIndices, data=data, fig=fig, verbose = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Confusion Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 495    0]\n",
      " [  16 7356]]\n"
     ]
    }
   ],
   "source": [
    "# Search for matches to rules\n",
    "matchingIndices = np.array([], dtype = 'int')\n",
    "for rule in rules:\n",
    "    difference = X - rule\n",
    "    mI = np.where(~difference.any(axis=1))[0]\n",
    "    matchingIndices = np.concatenate((matchingIndices, mI))\n",
    "\n",
    "#Make yHat vector, tells us which pixels our rules predict to be fingers.\n",
    "yHat = np.zeros(X.shape[0])\n",
    "yHat[matchingIndices] = 1\n",
    "\n",
    "#Count up False Negatives, False Positives, True Positives, and True Negatives\n",
    "FN =  np.sum(np.logical_and(y==1, yHat==0))\n",
    "FP =  np.sum(np.logical_and(y==0, yHat==1))\n",
    "TP = np.sum(np.logical_and(y==1, yHat==1))\n",
    "TN = np.sum(np.logical_and(y==0, yHat==0))\n",
    "    \n",
    "#make confusion matrix:\n",
    "confusionMatrix = np.array([[TP, FN], [FP, TN]])\n",
    "\n",
    "print confusionMatrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Precision and Recall:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 0.968688845401\n"
     ]
    }
   ],
   "source": [
    "recall = float(TP)/(TP+FN)\n",
    "precision = float(TP)/(TP+FP)\n",
    "\n",
    "print recall, precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(413, 81)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rules.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7867, 81)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7867,)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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