2016-08-24-notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UBC Scientific Software Seminar\n",
    "\n",
    "## August 24, 2016\n",
    "\n",
    "Today's Agenda:\n",
    "\n",
    "A basic machine learning example:\n",
    "\n",
    "* Digits dataset\n",
    "* Our own *k*-nearest neighbors classifier\n",
    "* Evaluating the classifier\n",
    "* Implementing `sklearn.neighbors.KNeighborsClassifier`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Digits dataset\n",
    "\n",
    "The [scikit-learn](http://scikit-learn.org/) package comes equipped with some toy [datasets](http://scikit-learn.org/stable/modules/classes.html#module-sklearn.datasets) to explore and, in this notebook, we'll look at the [digits dataset](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_digits.html). We import the `datasets` module and use the `load_digits` function to load the digits dataset. We can use `datasets.load_digits?` to consult the documentation to see what is returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "datasets.load_digits?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the documentation, the `load_digits` function returns a dictionary-like object which packages together several NumPy arrays and a description. To see what's available in the object, we can use the `.keys()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "digits = datasets.load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['DESCR', 'target', 'target_names', 'data', 'images'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optical Recognition of Handwritten Digits Data Set\n",
      "===================================================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 5620\n",
      "    :Number of Attributes: 64\n",
      "    :Attribute Information: 8x8 image of integer pixels in the range 0..16.\n",
      "    :Missing Attribute Values: None\n",
      "    :Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)\n",
      "    :Date: July; 1998\n",
      "\n",
      "This is a copy of the test set of the UCI ML hand-written digits datasets\n",
      "http://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits\n",
      "\n",
      "The data set contains images of hand-written digits: 10 classes where\n",
      "each class refers to a digit.\n",
      "\n",
      "Preprocessing programs made available by NIST were used to extract\n",
      "normalized bitmaps of handwritten digits from a preprinted form. From a\n",
      "total of 43 people, 30 contributed to the training set and different 13\n",
      "to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of\n",
      "4x4 and the number of on pixels are counted in each block. This generates\n",
      "an input matrix of 8x8 where each element is an integer in the range\n",
      "0..16. This reduces dimensionality and gives invariance to small\n",
      "distortions.\n",
      "\n",
      "For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.\n",
      "T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.\n",
      "L. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,\n",
      "1994.\n",
      "\n",
      "References\n",
      "----------\n",
      "  - C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their\n",
      "    Applications to Handwritten Digit Recognition, MSc Thesis, Institute of\n",
      "    Graduate Studies in Science and Engineering, Bogazici University.\n",
      "  - E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.\n",
      "  - Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.\n",
      "    Linear dimensionalityreduction using relevance weighted LDA. School of\n",
      "    Electrical and Electronic Engineering Nanyang Technological University.\n",
      "    2005.\n",
      "  - Claudio Gentile. A New Approximate Maximal Margin Classification\n",
      "    Algorithm. NIPS. 2000.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(digits.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the various arrays in the digits object. First, the **data array** is a 2D array where each row is a sample corresponding to a hand-written digit. We see that there are 1797 samples in the dataset each consisting of a 1D array of length 64 (representing an 8 by 8 pixel image)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.,   0.,   0.,  13.,\n",
       "        15.,  10.,  15.,   5.,   0.,   0.,   3.,  15.,   2.,   0.,  11.,\n",
       "         8.,   0.,   0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.,   0.,\n",
       "         5.,   8.,   0.,   0.,   9.,   8.,   0.,   0.,   4.,  11.,   0.,\n",
       "         1.,  12.,   7.,   0.,   0.,   2.,  14.,   5.,  10.,  12.,   0.,\n",
       "         0.,   0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data[0,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **target array** contains the label for each sample in data. We can see that the first sample is the digit 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **images array** is a 3D array which contains the same data as the data array but each sample is reshaped into a 8 by 8 array representing an 8 by 8 pixel image. In other words, the image array is simply a convenience so that we don't have to reshape the samples in the data array when we want to view the image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 8, 8)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.],\n",
       "       [  0.,   0.,  13.,  15.,  10.,  15.,   5.,   0.],\n",
       "       [  0.,   3.,  15.,   2.,   0.,  11.,   8.,   0.],\n",
       "       [  0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.],\n",
       "       [  0.,   5.,   8.,   0.,   0.,   9.,   8.,   0.],\n",
       "       [  0.,   4.,  11.,   0.,   1.,  12.,   7.,   0.],\n",
       "       [  0.,   2.,  14.,   5.,  10.,  12.,   0.,   0.],\n",
       "       [  0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.images[0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.],\n",
       "       [  0.,   0.,  13.,  15.,  10.,  15.,   5.,   0.],\n",
       "       [  0.,   3.,  15.,   2.,   0.,  11.,   8.,   0.],\n",
       "       [  0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.],\n",
       "       [  0.,   5.,   8.,   0.,   0.,   9.,   8.,   0.],\n",
       "       [  0.,   4.,  11.,   0.,   1.,  12.,   7.,   0.],\n",
       "       [  0.,   2.,  14.,   5.,  10.,  12.,   0.,   0.],\n",
       "       [  0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data[0,:].reshape(8,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f07d4c2ec50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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e8XgtrZbGgrkF6kO2ycHtjbes8Gyc56pH49ss6Pz8BH72OXdmQs2CegqNNTOE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\nEiRAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d4c14828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(digits.images[0,:,:],cmap='binary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **target_names array** is simply the complete list of labels for the samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "**Exercise.** Plot a 4 by 4 grid of randomly selected images from the dataset to get a sense of what the digits look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8UCUmHjnZe4ISydoac0dDzQqIl58R5aBMJhM3pKMEB78dIqEhxldjqBqbKxGS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\nUmm8EE5te13sPUGpxQb5c90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8mYLCjtojKKWJa7wHGYoFF7OX+L+ZLZSTFiJS+pxnvOXx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\nerIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d4dfdda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "indices = np.random.randint(0,1797,16) # Create an array of 16 random integers chosen from the interval [0,1797]\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "for i in range(0,16):\n",
    "    plt.subplot(4,4,i+1)\n",
    "    plt.imshow(digits.images[indices[i]],cmap='binary')\n",
    "    plt.title('Digit = {}'.format(digits.target[indices[i]]))\n",
    "    plt.axis('off')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Split the dataset into a training set and a testing set\n",
    "\n",
    "It's very important **not** to use the same data for constructing *and* testing your models for obvious reasons. It's [standard practice](http://scikit-learn.org/stable/tutorial/basic/tutorial.html) to split your dataset into a training set and a testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# N is arbitrarily chosen to be the size of the training dataset\n",
    "# (it may be better to take random sample of the dataset instead of the first N samples)\n",
    "N = 1200\n",
    "\n",
    "data_train = digits.data[:N,:]\n",
    "target_train = digits.target[:N]\n",
    "\n",
    "data_test = digits.data[N:,:]\n",
    "target_test = digits.target[N:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building our own *k*-nearest neighbors classifier\n",
    "\n",
    "[Nearest neighbors](http://scikit-learn.org/stable/modules/neighbors.html) refers to a family of classification and regression algorithms based on a simple principle: \"find a predefined number of training samples closest in distance to the new point, and predict the label from these\".\n",
    "\n",
    "Since the idea is simple enough, let's build our own classifier before we begin using sklearn implementations.\n",
    "\n",
    "#### Attempt 1: Build the classifier as a function\n",
    "\n",
    "Write a function which takes the following parameters:\n",
    "\n",
    "* `sample` - array of length 64 with values in the interval [0,16] (represnting an 8 by 8 pixel image of a digit)\n",
    "* `data` - array of samples of digits (as a 2D array of size (n samples) by 64)\n",
    "* `target` - array of labels for the samples in data\n",
    "* `k` - number of nearest neighbors to find"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def knn_predict(sample,data,target,k=1,output=False):\n",
    "    '''Predict digit label of sample using KNN with training samples in data with labels target.'''\n",
    "    \n",
    "    distances = np.linalg.norm(sample - data, axis=1)\n",
    "    sorted_distances = np.sort(distances)\n",
    "    threshold = sorted_distances[k - 1]\n",
    "    neighbors = target[distances <= threshold]\n",
    "    prediction = np.bincount(neighbors).argmax()\n",
    "    \n",
    "    if output:\n",
    "        plt.imshow(sample.reshape(8,8),cmap='binary')\n",
    "        plt.title('Sample Image')\n",
    "        plt.axis('off')\n",
    "        plt.show()\n",
    "\n",
    "        print(k,'nearest neighbors are:',neighbors)\n",
    "\n",
    "        print('\\nKNN predicts:',prediction)\n",
    "    \n",
    "    return prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PXhbJ6oxt28lRbXfUPj1Wu6oK7JHFR/Ho+HvqJOAW4S+ZqBDoKJ/K3mGtJa/A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\nT00dVBPuqamDasI9NXVQTbinpg6q/w9mLEJ2elz4YgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d1ddaef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 nearest neighbors are: [9 9 9 9 9 9 9]\n",
      "\n",
      "KNN predicts: 9\n",
      "\n",
      "Digit is: 9\n"
     ]
    }
   ],
   "source": [
    "i = np.random.randint(0,len(data_test)) # Choose a random index in the test data\n",
    "knn_predict(data_test[i,:],data_train,target_train,k=7,output=True)\n",
    "print('\\nDigit is:',target_test[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Attempt 2: Build the classifier as an object\n",
    "\n",
    "Write a class which produces objects with:\n",
    "\n",
    "Attributes:\n",
    "\n",
    "* `data` - array of training samples of digits (as a 2D array of size (n samples) by 64)\n",
    "* `target` - array of training labels for the samples in data\n",
    "* `k` - number of neighbors in KNN algorithm\n",
    "\n",
    "Methods:\n",
    "\n",
    "* `__init__` - instantiates an object\n",
    "* `fit` - creates a model ready for prediction\n",
    "* `predict` - takes an sample (as an array of length 64) and predicts the digit based on the KNN model\n",
    "* `score` - takes arrays of images and labels and returns the accuracy of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class KNN():\n",
    "    \n",
    "    def __init__(self,k=10):\n",
    "        self.k = k\n",
    "        print('Creating KNN classifier object with k = {} ...'.format(self.k))\n",
    "    \n",
    "    def fit(self,data_train,target_train):\n",
    "        self.data = data_train\n",
    "        self.target = target_train\n",
    "        print('Fitting the model with',self.data.shape[0],'training samples ...')\n",
    "    \n",
    "    def predict(self,sample,output=False):\n",
    "        distances = np.linalg.norm(sample - self.data, axis=1)\n",
    "        sorted_distances = np.sort(distances)\n",
    "        threshold = sorted_distances[self.k - 1]\n",
    "        neighbors = self.target[distances <= threshold]\n",
    "        prediction = np.bincount(neighbors).argmax()\n",
    "\n",
    "        if output:\n",
    "            plt.imshow(sample.reshape(8,8),cmap='binary')\n",
    "            plt.title('Sample Image')\n",
    "            plt.axis('off')\n",
    "            plt.show()\n",
    "            print(self.k,'nearest neighbors are:',neighbors)\n",
    "            print('\\nKNN predicts:',prediction)\n",
    "    \n",
    "        return prediction\n",
    "    \n",
    "    def score(self,test_data,test_target):\n",
    "        n_samples = test_data.shape[0]\n",
    "        predictions = np.array([])\n",
    "        for image in test_data:\n",
    "            prediction = self.predict(image)\n",
    "            predictions = np.append(predictions,prediction)\n",
    "        \n",
    "        correct = predictions[predictions == test_target]\n",
    "        accuracy = len(correct) / n_samples\n",
    "        return accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating KNN classifier object with k = 7 ...\n",
      "Fitting the model with 1200 training samples ...\n"
     ]
    }
   ],
   "source": [
    "clf = KNN(k=7)\n",
    "clf.fit(data_train,target_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GVjebEVnDri3jtlTBTfoF3ypO/ippBnALcgt4Pl9kfUcWPIbn4nvlzkAugdYA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d1fba710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 nearest neighbors are: [2 2 2 2 2 2 2]\n",
      "\n",
      "KNN predicts: 2\n",
      "\n",
      "Digit is: 2\n"
     ]
    }
   ],
   "source": [
    "i = np.random.randint(0,len(data_test)) # Choose a random index in the test data\n",
    "clf.predict(data_test[i,:],output=True)\n",
    "print('\\nDigit is:',target_test[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WHOFmsCO33LPc2sbapl57lgb7aLt5r+V6Vrsm13yRcAPHwyata+5Zbe+m8wBX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d204fba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20 nearest neighbors are: [8 8 8 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8]\n",
      "\n",
      "KNN predicts: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0 = [0,0,0,15,15,0,0,0]\n",
    "v1 = [0,0,15,0,0,15,0,0]\n",
    "v2 = [0,0,15,0,0,15,0,0]\n",
    "v3 = [0,0,0,15,15,0,0,0]\n",
    "v4 = [0,0,0,15,15,0,0,0]\n",
    "v5 = [0,0,15,0,0,15,0,0]\n",
    "v6 = [0,0,15,0,0,15,0,0]\n",
    "v7 = [0,0,0,15,15,0,0,0]\n",
    "\n",
    "clf.k = 20\n",
    "image = np.array([v0,v1,v2,v3,v4,v5,v6,v7]).reshape(64,)\n",
    "clf.predict(image,output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the model\n",
    "\n",
    "Recall that we split the dataset in two parts: a training set and a testing set. The idea is that we want to evaluate the accuracy of our model but **we can't test the model on the data we used to train the model** and so we use the testing set to evaluate the accuracy of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating KNN classifier object with k = 7 ...\n",
      "Fitting the model with 1200 training samples ...\n"
     ]
    }
   ],
   "source": [
    "clf = KNN(k=7)\n",
    "clf.fit(data_train,target_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9631490787269682"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.score(data_test,target_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating KNN classifier object with k = 1 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 1  accuracy is 0.964824120603015\n",
      "Creating KNN classifier object with k = 2 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 2  accuracy is 0.9681742043551089\n",
      "Creating KNN classifier object with k = 3 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 3  accuracy is 0.9698492462311558\n",
      "Creating KNN classifier object with k = 4 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 4  accuracy is 0.964824120603015\n",
      "Creating KNN classifier object with k = 5 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 5  accuracy is 0.964824120603015\n",
      "Creating KNN classifier object with k = 6 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 6  accuracy is 0.9614740368509213\n",
      "Creating KNN classifier object with k = 7 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 7  accuracy is 0.9631490787269682\n",
      "Creating KNN classifier object with k = 8 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 8  accuracy is 0.9597989949748744\n",
      "Creating KNN classifier object with k = 9 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 9  accuracy is 0.9614740368509213\n",
      "Creating KNN classifier object with k = 10 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 10  accuracy is 0.9581239530988275\n",
      "Creating KNN classifier object with k = 11 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 11  accuracy is 0.9547738693467337\n",
      "Creating KNN classifier object with k = 12 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 12  accuracy is 0.9530988274706867\n",
      "Creating KNN classifier object with k = 13 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 13  accuracy is 0.9530988274706867\n",
      "Creating KNN classifier object with k = 14 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 14  accuracy is 0.9530988274706867\n",
      "Creating KNN classifier object with k = 15 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 15  accuracy is 0.9547738693467337\n",
      "Creating KNN classifier object with k = 16 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 16  accuracy is 0.9514237855946399\n",
      "Creating KNN classifier object with k = 17 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 17  accuracy is 0.9514237855946399\n",
      "Creating KNN classifier object with k = 18 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 18  accuracy is 0.9547738693467337\n",
      "Creating KNN classifier object with k = 19 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 19  accuracy is 0.9547738693467337\n",
      "Creating KNN classifier object with k = 20 ...\n",
      "Fitting the model with 1200 training samples ...\n",
      "For k = 20  accuracy is 0.9530988274706867\n"
     ]
    }
   ],
   "source": [
    "for k in range(1,21):\n",
    "    clf = KNN(k=k);\n",
    "    clf.fit(data_train,target_train);\n",
    "    print('For k =',k,' accuracy is',clf.score(data_test,target_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that `k = 3` produces the best results with 96.48% accuracy:\n",
    "\n",
    "```\n",
    "Creating KNN classifier object with k = 3 ...\n",
    "Fitting the model with 1200 training samples ...\n",
    "For k = 3  accuracy is 0.9698492462311558\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use k = 3 on some digits created manually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d1f6f358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 nearest neighbors are: [9 9 9]\n",
      "\n",
      "KNN predicts: 9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0 = [0,0,15,15,15,15,0,0]\n",
    "v1 = [0,0,15,0,0,15,0,0]\n",
    "v2 = [0,0,15,0,0,15,0,0]\n",
    "v3 = [0,0,15,15,15,15,0,0]\n",
    "v4 = [0,0,0,0,0,15,0,0]\n",
    "v5 = [0,0,0,0,0,15,0,0]\n",
    "v6 = [0,0,15,0,0,15,0,0]\n",
    "v7 = [0,0,15,15,15,15,0,0]\n",
    "\n",
    "clf.k = 3\n",
    "image = np.array([v0,v1,v2,v3,v4,v5,v6,v7]).reshape(64,)\n",
    "clf.predict(image,output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing `sklearn.neighbors.KNeighborsClassifier`\n",
    "\n",
    "See the [documentation](http://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html) for a description of the *k*-nearest neighbors class and its attributes and methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier as KNC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "clf = KNC(n_neighbors=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "           metric_params=None, n_jobs=1, n_neighbors=3, p=2,\n",
       "           weights='uniform')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.fit(data_train,target_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sn6XPn5dtKCcRJ2Gn9fw15eQiEe3rknsuP60VOyRvY7FycyJP5RNc9zxHEht4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\nHQRbSsgdBFvK/wNY+D7/DL5oLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07d007a6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier predicts: 1\n",
      "Digit is: 1\n"
     ]
    }
   ],
   "source": [
    "i = np.random.randint(0,len(data_test)) # Choose a random index in the test data\n",
    "plt.imshow(data_test[i].reshape(8,8),cmap='binary')\n",
    "plt.show()\n",
    "prediction = clf.predict(data_test[i].reshape(1,64)) # All sklearn models expect a 2D array input to the predict method\n",
    "print('Classifier predicts:',prediction[0])\n",
    "print('Digit is:',target_test[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96984924623115576"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.score(data_test,target_test)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}