{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines\n",
    "\n",
    "\n",
    "In this notebook we gain some visual intuition on how Support Vector Machine (SVM) classifiers work with a dataset in 2 dimensions, and then build a spam classifier with SVMs!\n",
    "\n",
    "![Kernel Machine](notebooks/svm-files/Kernel_Machine.png?raw=true \"Kernel Machine\")\n",
    "\n",
    "SVMs help us look at our training examples and learn a way to map them to a high-dimensional space so that we can separate different categories with boundaries that are as wide as possible (as in the image above). When a new example comes along, we can map it to that space and categorize it based on which side of the boundaries it falls on. \n",
    "\n",
    "This mapping is possible due to a [_kernel_](https://en.wikipedia.org/wiki/Kernel_method) function. This is the function that maps the examples into a high-dimensional space. Use of kernel functions are often called kernel tricks because we don't need to know the exact mapping of the examples into that space (which can be expensive to compute), but rather only the _similarity_ between those mappings (which can be cheaper to compute).\n",
    "\n",
    "Even if this is all a bit fuzzy, SVMs are important to know and interesting to look at because they have been a [popular](https://www.quora.com/Why-did-SVM-become-more-popular-than-Logistic-Regression) [black-box](https://datascience.stackexchange.com/questions/711/are-support-vector-machines-still-considered-state-of-the-art-in-their-niche) [choice](https://www.researchgate.net/post/Can_we_say_that_SVM_is_the_best_classifier_to_date14) for machine learning practitioners.\n",
    "\n",
    "You can find this code in modules [here](https://github.com/arturomp/coursera-machine-learning-in-python/tree/master/mlclass-ex6-004/mlclass-ex6), along with the files used.\n",
    "\n",
    "This code was ported from Octave/Matlab to python and was part of the absolutely excellent [Machine Learning course](http://ml-class.org) by Stanford's [Andrew Ng](http://www.andrewng.org) on Coursera.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import scipy.io\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import svm\n",
    "import re\n",
    "from nltk import PorterStemmer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "\n",
    "We can start by visualizing our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plotData(X, y):\n",
    "    \"\"\"Plots the data points X and y into a new figure \"\"\"\n",
    "    \n",
    "    y = y.flatten()\n",
    "    pos = y==1\n",
    "    neg = y==0\n",
    "    \n",
    "    plt.plot(X[:,0][pos], X[:,1][pos], \"k+\", markersize=15, mew=3)\n",
    "    plt.plot(X[:,0][neg], X[:,1][neg], \"yo\", markersize=15)\n",
    "\n",
    "    # shorter but not as clear\n",
    "    # plt.plot(X[:,0][pos], X[:,1][pos], 'k+', X[:,0][neg], X[:,1][neg], 'yo', markersize=15)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
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e1djYBa2sfCRptUVaV9cR5fMHCZRAnSEwpAu/r/Jx7eJHOEbdKRQuaWLinFpabmrv3rtq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\nShmEF2TcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ac1590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('notebooks/svm-files/ex6data1.mat')\n",
    "X = mat[\"X\"]\n",
    "y = mat[\"y\"]\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plotData(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear kernel SVM\n",
    "\n",
    "Now we can load ``svmTrain()``, a wrapper function to train a SVM. It's defined to accept other kernels moving forward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def svmTrain(X, y, C, kernelFunction, tol=1e-3, max_passes=-1, sigma=0.1):\n",
    "    \"\"\"Trains an SVM classifier\"\"\"\n",
    "    \n",
    "    y = y.flatten()\n",
    "\n",
    "    if kernelFunction == \"gaussian_rbf\":\n",
    "        clf = svm.SVC(C = C, kernel=\"precomputed\", tol=tol, max_iter=max_passes, verbose=2)\n",
    "        return clf.fit(gaussianKernelGramMatrix(X,X, sigma=sigma), y)\n",
    "    \n",
    "    else: \n",
    "        clf = svm.SVC(C = C, kernel=kernelFunction, tol=tol, max_iter=max_passes, verbose=2)\n",
    "        return clf.fit(X, y)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also define a function to visualize the linear boundary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def visualizeBoundaryLinear(X, y, model):\n",
    "    \"\"\"Plots a linear decision boundary learned by the SVM\"\"\"\n",
    "    \n",
    "    plt.figure(figsize=(12,8))\n",
    "    w = model.coef_[0]\n",
    "    b = model.intercept_[0]\n",
    "    xp = np.linspace(X[:,0].min(), X[:,0].max(), 100)\n",
    "    yp = - (w[0] * xp + b) / w[1]\n",
    "\n",
    "    plt.plot(xp, yp, 'b-')    \n",
    "    plotData(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can train a linear SVM and plot the decision boundary learned:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[LibSVM]"
     ]
    },
    {
     "data": {
      "image/png": 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ili59mAULZtDS8joQj0gbMGA41dX9TSiVl9ati8e/3XsvXHklXHUVdOqUdFSF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\nVFgcS5IkSYXFsSRJklRYHEuSJEnFLwD1aIS7KXblcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11678cc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = 1\n",
    "model = svmTrain(X, y, C, \"linear\", 1e-3, 20)\n",
    "visualizeBoundaryLinear(X, y, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also try a different value for ``C``, the parameter that tells the linear SVM \"how much you want to avoid misclassifying each training example\" [(as stated here)](https://stats.stackexchange.com/a/31067/19809). That is, it's a penalty for misclassified examples.\n",
    "\n",
    "You can also see great visual representations the effects of low and high ``C`` values on different datasets [here](https://stats.stackexchange.com/a/159051/19809).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[LibSVM]"
     ]
    },
    {
     "data": {
      "image/png": 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GrPCGh09l1Xu1slKjLeoA5F6QC82m+jcx/UIzM2n+fO92551jj3FOeu+98YH5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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11493cc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C = 100\n",
    "model = svmTrain(X, y, C, \"linear\", 1e-3, 20)\n",
    "visualizeBoundaryLinear(X, y, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that, in an effort to accommodate the outlier around (0,4), the ``C=100`` boundary performs worse than with ``C=1``.\n",
    "\n",
    "## Gaussian Kernel SVM\n",
    "\n",
    "We extend our SVM capabilities by defining a Gaussian RBF kernel. In case you're curious, here's a more detailed explanation of the [difference between a Gaussian kernel and a Gaussian _RBF_ kernel](https://stats.stackexchange.com/questions/79192/gaussian-rbf-vs-gaussian-kernel). Roughly, the Gaussian RBF kernel used here helps us measure the distance or the similarity between a pair of examples. \n",
    "\n",
    "We use a ``sigma`` parameter that indicates how quickly the similarity metric decreases as two examples are further apart.\n",
    "\n",
    "Using a custom kernel with [``sklearn.svm.SCV()``](http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html) was not as well documented as I'd hoped, so I put up an [answer about it](https://stackoverflow.com/a/38647546/583834) in Stack Overflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gaussianKernel(x1, x2, sigma=0.1):\n",
    "    \"\"\"returns a (gaussian) radial basis function kernel between x1 and x2\"\"\"\n",
    "    \n",
    "    x1 = x1.flatten()\n",
    "    x2 = x2.flatten()\n",
    "    sim = np.exp(- np.sum( np.power((x1 - x2),2) ) / float( 2*(sigma**2) ) )\n",
    "\n",
    "    return sim\n",
    "\n",
    "def gaussianKernelGramMatrix(X1, X2, K_function=gaussianKernel, sigma=0.1):\n",
    "    \"\"\"(Pre)calculates Gram Matrix K\"\"\"\n",
    "\n",
    "    gram_matrix = np.zeros((X1.shape[0], X2.shape[0]))\n",
    "    for i, x1 in enumerate(X1):\n",
    "        for j, x2 in enumerate(X2):\n",
    "            gram_matrix[i, j] = K_function(x1, x2, sigma)\n",
    "    return gram_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We evaluate the implementation of ``gaussianKernel()``. The output should be about 0.324652."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian Kernel between x1 = [1 2 1] , x2 = [ 0  4 -1] , sigma = 2 :\n",
      "0.324652\n"
     ]
    }
   ],
   "source": [
    "x1 = np.array([1, 2, 1])\n",
    "x2 = np.array([0, 4, -1])\n",
    "sigma = 2\n",
    "sim = gaussianKernel(x1, x2, sigma)\n",
    "\n",
    "print(\"Gaussian Kernel between x1 =\", x1, \", x2 =\", x2, \", sigma =\", sigma, \":\\n{:f}\".format(sim))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A more complex dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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++WQQ8vOLcMEFo7Bv346u8/pZ0lY0NlOPH7GWdsiIl/fSnhkiXi1ZOQ1B4acB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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1104fda10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('notebooks/svm-files/ex6data2.mat')\n",
    "X = mat[\"X\"]\n",
    "y = mat[\"y\"]\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plotData(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to visualize the SVM-trained boundaries around the data categories, we define a new visualization function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def visualizeBoundary(X, y, model, varargin=0):\n",
    "    \"\"\"Plots a non-linear decision boundary learned by the SVM\"\"\"\n",
    "    \n",
    "    plt.figure(figsize=(12,8))\n",
    "\n",
    "    x1plot = np.linspace(X[:,0].min(), X[:,0].max(), 100).T\n",
    "    x2plot = np.linspace(X[:,1].min(), X[:,1].max(), 100).T\n",
    "    X1, X2 = np.meshgrid(x1plot, x2plot)\n",
    "    vals = np.zeros(X1.shape)\n",
    "    for i in xrange(X1.shape[1]):\n",
    "       this_X = np.column_stack((X1[:, i], X2[:, i]))\n",
    "       vals[:, i] = model.predict(gaussianKernelGramMatrix(this_X, X))\n",
    "\n",
    "    plt.contour(X1, X2, vals, colors=\"blue\", levels=[0,0], linewidth=5)\n",
    "    \n",
    "    plotData(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can train a SVM with a Gaussian RBF kernel and visualize the boundaries it learns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[LibSVM]"
     ]
    }
   ],
   "source": [
    "C = 1\n",
    "sigma = 0.1\n",
    "\n",
    "model = svmTrain(X, y, C, \"gaussian_rbf\", sigma=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/ZXJma9aYG79xw80OkZccAafqc1HB73E/yvj521P5usaF2BvAPFD8jzz0Cw4r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FSSBEhZMi1tBt5773ns2bNblfOo58h37txNyM7+CmE0NVyT4OUHbt8ejg4d4piaX7T4okbuhM2a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\nCIIgCCKl+P+pDDwDf5TcPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116832fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualizeBoundary(X, y, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizing SVM parameters\n",
    "\n",
    "Now we consider a third dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i8QiJxBymp/swOHiPpSYrmHhwQc41hL0AIiInSuOWVQ9SVJHJZCClXPVVrtLv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116a9e2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('notebooks/svm-files/ex6data3.mat')\n",
    "X = mat[\"X\"]\n",
    "y = mat[\"y\"]\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plotData(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can try different parameters on a validation set to find a good fit for the trained boundaries. We define a function to explore the range {0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30} for ``C`` and ``sigma``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dataset3Params(X, y, Xval, yval):\n",
    "    \"\"\"returns optimal C and sigma found in the cross validation set\"\"\"\n",
    "    \n",
    "    predictionErrors = np.zeros((64,3))\n",
    "    predictionsCounter = 0\n",
    "\n",
    "    for sigma in [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30]:\n",
    "        for C in [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30]:\n",
    "\n",
    "            print(\" trying C={:.2f}, sigma={:.2f},\".format(C, sigma), end=\"...\")\n",
    "            \n",
    "            model = svmTrain(X, y, C, \"gaussian_rbf\", sigma=sigma)\n",
    "\n",
    "            predictions = model.predict(gaussianKernelGramMatrix(Xval, X))\n",
    "\n",
    "            predictionErrors[predictionsCounter,0] = np.mean((predictions != yval).astype(int))\n",
    "\n",
    "            predictionErrors[predictionsCounter,1] = C      \n",
    "            predictionErrors[predictionsCounter,2] = sigma\n",
    "            \n",
    "            predictionsCounter = predictionsCounter + 1\n",
    "\n",
    "    print()\n",
    "    \n",
    "    # sort ndarray by first column, from https://stackoverflow.com/a/2828121/583834\n",
    "    predictionErrors = predictionErrors[predictionErrors[:,0].argsort()]\n",
    "    \n",
    "    print('\\t# Pred. error\\tsigma\\tC\\n')\n",
    "    for i in xrange(predictionErrors.shape[0]):\n",
    "        pred_error, sigma, C, = predictionErrors[i][:]\n",
    "        print('  \\t{:f}\\t{:.2f}\\t{:.2f}'.format(pred_error, sigma, C))\n",
    "\n",
    "    C     = predictionErrors[0,1]\n",
    "    sigma = predictionErrors[0,2]\n",
    "\n",
    "    return C, sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we run it to find the optimal values of ``C`` and ``sigma``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " trying C=0.01, sigma=0.01,...[LibSVM] trying C=0.03, sigma=0.01,...[LibSVM] trying C=0.10, sigma=0.01,...[LibSVM] trying C=0.30, sigma=0.01,...[LibSVM] trying C=1.00, sigma=0.01,...[LibSVM] trying C=3.00, sigma=0.01,...[LibSVM] trying C=10.00, sigma=0.01,...[LibSVM] trying C=30.00, sigma=0.01,...[LibSVM] trying C=0.01, sigma=0.03,...[LibSVM] trying C=0.03, sigma=0.03,...[LibSVM] trying C=0.10, sigma=0.03,...[LibSVM] trying C=0.30, sigma=0.03,...[LibSVM] trying C=1.00, sigma=0.03,...[LibSVM] trying C=3.00, sigma=0.03,...[LibSVM] trying C=10.00, sigma=0.03,...[LibSVM] trying C=30.00, sigma=0.03,...[LibSVM] trying C=0.01, sigma=0.10,...[LibSVM] trying C=0.03, sigma=0.10,...[LibSVM] trying C=0.10, sigma=0.10,...[LibSVM] trying C=0.30, sigma=0.10,...[LibSVM] trying C=1.00, sigma=0.10,...[LibSVM] trying C=3.00, sigma=0.10,...[LibSVM] trying C=10.00, sigma=0.10,...[LibSVM] trying C=30.00, sigma=0.10,...[LibSVM] trying C=0.01, sigma=0.30,...[LibSVM] trying C=0.03, sigma=0.30,...[LibSVM] trying C=0.10, sigma=0.30,...[LibSVM] trying C=0.30, sigma=0.30,...[LibSVM] trying C=1.00, sigma=0.30,...[LibSVM] trying C=3.00, sigma=0.30,...[LibSVM] trying C=10.00, sigma=0.30,...[LibSVM] trying C=30.00, sigma=0.30,...[LibSVM] trying C=0.01, sigma=1.00,...[LibSVM] trying C=0.03, sigma=1.00,...[LibSVM] trying C=0.10, sigma=1.00,...[LibSVM] trying C=0.30, sigma=1.00,...[LibSVM] trying C=1.00, sigma=1.00,...[LibSVM] trying C=3.00, sigma=1.00,...[LibSVM] trying C=10.00, sigma=1.00,...[LibSVM] trying C=30.00, sigma=1.00,...[LibSVM] trying C=0.01, sigma=3.00,...[LibSVM] trying C=0.03, sigma=3.00,...[LibSVM] trying C=0.10, sigma=3.00,...[LibSVM] trying C=0.30, sigma=3.00,...[LibSVM] trying C=1.00, sigma=3.00,...[LibSVM] trying C=3.00, sigma=3.00,...[LibSVM] trying C=10.00, sigma=3.00,...[LibSVM] trying C=30.00, sigma=3.00,...[LibSVM] trying C=0.01, sigma=10.00,...[LibSVM] trying C=0.03, sigma=10.00,...[LibSVM] trying C=0.10, sigma=10.00,...[LibSVM] trying C=0.30, sigma=10.00,...[LibSVM] trying C=1.00, sigma=10.00,...[LibSVM] trying C=3.00, sigma=10.00,...[LibSVM] trying C=10.00, sigma=10.00,...[LibSVM] trying C=30.00, sigma=10.00,...[LibSVM] trying C=0.01, sigma=30.00,...[LibSVM] trying C=0.03, sigma=30.00,...[LibSVM] trying C=0.10, sigma=30.00,...[LibSVM] trying C=0.30, sigma=30.00,...[LibSVM] trying C=1.00, sigma=30.00,...[LibSVM] trying C=3.00, sigma=30.00,...[LibSVM] trying C=10.00, sigma=30.00,...[LibSVM] trying C=30.00, sigma=30.00,...[LibSVM]\n",
      "\t# Pred. error\tsigma\tC\n",
      "\n",
      "  \t0.489600\t0.10\t0.10\n",
      "  \t0.490250\t10.00\t0.10\n",
      "  \t0.490250\t1.00\t0.03\n",
      "  \t0.490900\t10.00\t30.00\n",
      "  \t0.490900\t3.00\t0.10\n",
      "  \t0.490900\t3.00\t10.00\n",
      "  \t0.490900\t30.00\t0.03\n",
      "  \t0.490900\t10.00\t0.03\n",
      "  \t0.490900\t3.00\t0.03\n",
      "  \t0.490900\t10.00\t10.00\n",
      "  \t0.490900\t30.00\t30.00\n",
      "  \t0.490900\t30.00\t0.01\n",
      "  \t0.490900\t10.00\t0.01\n",
      "  \t0.490900\t3.00\t0.01\n",
      "  \t0.490900\t1.00\t0.01\n",
      "  \t0.491550\t0.30\t0.03\n",
      "  \t0.491550\t3.00\t30.00\n",
      "  \t0.491550\t0.03\t0.30\n",
      "  \t0.492200\t1.00\t3.00\n",
      "  \t0.492200\t1.00\t0.10\n",
      "  \t0.492200\t30.00\t10.00\n",
      "  \t0.492850\t0.10\t0.30\n",
      "  \t0.492850\t30.00\t0.10\n",
      "  \t0.492850\t0.30\t0.10\n",
      "  \t0.496100\t1.00\t10.00\n",
      "  \t0.496100\t0.30\t3.00\n",
      "  \t0.497400\t1.00\t30.00\n",
      "  \t0.498700\t0.10\t1.00\n",
      "  \t0.500650\t3.00\t3.00\n",
      "  \t0.507150\t0.30\t0.01\n",
      "  \t0.507150\t0.30\t1.00\n",
      "  \t0.509750\t10.00\t3.00\n",
      "  \t0.512350\t0.30\t10.00\n",
      "  \t0.512350\t0.30\t0.30\n",
      "  \t0.512350\t0.30\t30.00\n",
      "  \t0.513000\t30.00\t3.00\n",
      "  \t0.514950\t1.00\t1.00\n",
      "  \t0.516250\t30.00\t0.30\n",
      "  \t0.519500\t30.00\t1.00\n",
      "  \t0.519500\t10.00\t0.30\n",
      "  \t0.520150\t3.00\t1.00\n",
      "  \t0.522100\t10.00\t1.00\n",
      "  \t0.529250\t3.00\t0.30\n",
      "  \t0.529900\t0.10\t0.03\n",
      "  \t0.530550\t0.10\t3.00\n",
      "  \t0.530550\t1.00\t0.30\n",
      "  \t0.539000\t0.10\t0.01\n",
      "  \t0.543550\t0.10\t10.00\n",
      "  \t0.544850\t0.10\t30.00\n",
      "  \t0.560450\t0.03\t1.00\n",
      "  \t0.563050\t0.03\t0.10\n",
      "  \t0.565000\t0.01\t10.00\n",
      "  \t0.565000\t0.03\t10.00\n",
      "  \t0.565000\t0.01\t0.30\n",
      "  \t0.565000\t0.01\t0.10\n",
      "  \t0.565000\t0.03\t3.00\n",
      "  \t0.565000\t0.03\t0.03\n",
      "  \t0.565000\t0.01\t30.00\n",
      "  \t0.565000\t0.03\t30.00\n",
      "  \t0.565000\t0.01\t0.03\n",
      "  \t0.565000\t0.01\t3.00\n",
      "  \t0.565000\t0.03\t0.01\n",
      "  \t0.565000\t0.01\t1.00\n",
      "  \t0.565000\t0.01\t0.01\n",
      "Best parameters are C=0.10, sigma=0.10\n"
     ]
    }
   ],
   "source": [
    "Xval = mat[\"Xval\"]\n",
    "yval = mat[\"yval\"]\n",
    "\n",
    "C, sigma = dataset3Params(X, y, Xval, yval)\n",
    "print(\"Best parameters are C={:.2f}, sigma={:.2f}\".format(C, sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we use these parameters to train a SVM model and visualize its boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[LibSVM]"
     ]
    },
    {
     "data": {
      "image/png": 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7/ZhubOzhx3xQeYRqi3GEEFK1MZEzuAhsIS/mJJlMFm1lU0xXV1dgg2QnufU6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\nRERERMooQBYRERERKfP/SWXaJQEqmZAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116be2150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = svmTrain(X, y, C, \"gaussian_rbf\", sigma=sigma)\n",
    "visualizeBoundary(X, y, model)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spam classifier\n",
    "\n",
    "Now that we've applied SVMs to datasets and tuned their parameters, we can apply them to a more real-world application: spam classification (or curation ;).\n",
    "\n",
    "![Is this real life](notebooks/svm-files/Spam_Museum.jpg?raw=true \"Spam Museum\")\n",
    "\n",
    "\n",
    "With a trained SVM we'll determine whether an unseen email is spam (``y=1``) or not spam (``y=0``).\n",
    "\n",
    "## Vectorizing emails\n",
    "\n",
    "In order to turn email text into training data that we can use in an SVM, we first need to establish a pipeline to turn each of the emails into a feature vector.\n",
    "\n",
    "The data we'll be working with comes from the [SpamAssassin Public Corpus](http://csmining.org/index.php/spam-assassin-datasets.html) and contains only the body of the email (without the headers).\n",
    "\n",
    "Doing some data exploration can help us see how we can process these emails to eventually vectorize them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def readFile(filename):\n",
    "    \"\"\"reads a file and returns its entire contents \"\"\"\n",
    "    try:\n",
    "        with open(filename, 'r') as openFile:\n",
    "            file_contents = openFile.read()\n",
    "    except:\n",
    "        file_contents = ''\n",
    "        print('Unable to open {:s}'.format(filename))\n",
    "\n",
    "    return file_contents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Anyone knows how much it costs to host a web portal ?\n",
      ">\n",
      "Well, it depends on how many visitors you're expecting.\n",
      "This can be anywhere from less than 10 bucks a month to a couple of $100. \n",
      "You should checkout http://www.rackspace.com/ or perhaps Amazon EC2 \n",
      "if youre running something big..\n",
      "\n",
      "To unsubscribe yourself from this mailing list, send an email to:\n",
      "groupname-unsubscribe@egroups.com\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "file_contents = readFile('notebooks/svm-files/emailSample1.txt')\n",
    "print(file_contents)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature engineering\n",
    "\n",
    "Items like email addresses, URLs, numbers and dollar amounts can be normalized. Different emails make reference to distinct specific addresses and amounts, but for our purposes it makes sense to treat them all as the same kind of entity. \n",
    "\n",
    "For instance, we can replace all URLs for the string ``httpaddr`` to indicate that the email had a URL at that location. This makes it possible for the presence or absence of a URL to be a feature to be used by the spam classifier, instead of having a feature for every URL possible. Given that spam emails tend to use odd, unique-looking URLs, we can save a lot of features with normalization.\n",
    "\n",
    "Normalizing text this way usually has the effect of [improving classifier performance](https://nlp.stanford.edu/IR-book/html/htmledition/features-for-text-1.html).\n",
    "\n",
    "Choosing which words we use in the classifier is also important. For this exercise, the most frequent words have already been selected and are included in ``vocab.txt``. Rare words that occur only in a few emails could throw the classifier off by causing it to overfit. The vocabulary list was chosen by selecting words with a minimum frequency of 100 across the whole SpamAssassin corpus. Our feature set consists of only 1899 words, but in the real world we can easily have vocabulary lists of tens of thousands of tokens.\n",
    "\n",
    "See the comments on the preprocessing code below to see more details on how each email is processed and normalized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def getVocabList():\n",
    "    \"\"\"reads the fixed vocabulary list in vocab.txt and returns a\n",
    "    cell array of the words\n",
    "    \"\"\"\n",
    "    \n",
    "    with open('notebooks/svm-files/vocab.txt', 'r') as vocabFile:\n",
    "        vocabList = {}\n",
    "        for line in vocabFile.readlines():\n",
    "            i, word = line.split()\n",
    "            vocabList[word] = int(i)\n",
    "\n",
    "    return vocabList\n",
    "\n",
    "def processEmail(email_contents, verbose=True):\n",
    "    \"\"\"preprocesses a the body of an email and\n",
    "    returns a list of word_indices \n",
    "    \"\"\"\n",
    "    vocabList = getVocabList()\n",
    "\n",
    "    # Init return value\n",
    "    word_indices = []\n",
    "\n",
    "    # ========================== Preprocess Email ===========================\n",
    "\n",
    "    # Find the Headers ( \\n\\n and remove )\n",
    "    # Uncomment the following lines if you are working with raw emails with the\n",
    "    # full headers\n",
    "\n",
    "    # hdrstart = email_contents.find(\"\\n\\n\")\n",
    "    # if hdrstart:\n",
    "    #     email_contents = email_contents[hdrstart:]\n",
    "\n",
    "    # Lower case\n",
    "    email_contents = email_contents.lower()\n",
    "\n",
    "    # Strip all HTML\n",
    "    # Looks for any expression that \n",
    "    # - starts with < and ends with >, &\n",
    "    # - does not have any < or > in the tag \n",
    "    # and replace it with a space \n",
    "    email_contents = re.sub('<[^<>]+>', ' ', email_contents)\n",
    "\n",
    "    # Handle Numbers\n",
    "    # Look for one or more characters between 0-9 and replace it with 'number'\n",
    "    email_contents = re.sub('[0-9]+', 'number', email_contents)\n",
    "\n",
    "    # Handle URLS\n",
    "    # Look for strings starting with http:// or https://\n",
    "    # and replace with 'httpaddr'\n",
    "    email_contents = re.sub('(http|https)://[^\\s]*', 'httpaddr', email_contents)\n",
    "\n",
    "    # Handle Email Addresses\n",
    "    # Look for strings with @ in the middle\n",
    "    # and replace with 'emailaddr'\n",
    "    email_contents = re.sub('[^\\s]+@[^\\s]+', 'emailaddr', email_contents)\n",
    "\n",
    "    # Handle $ sign\n",
    "    # replace with 'dollar'\n",
    "    email_contents = re.sub('[$]+', 'dollar', email_contents)\n",
    "\n",
    "\n",
    "    # Output the email to screen as well\n",
    "    if verbose: print('\\n==== Processed Email ====\\n\\n')\n",
    "\n",
    "    l = 0\n",
    "\n",
    "    # Split and also get rid of any punctuation\n",
    "    # regex may need further debugging...\n",
    "    email_contents = re.split(r'[@$/#.-:&\\*\\+=\\[\\]?!(){},\\'\\'\\\">_<;%\\s\\n\\r\\t]+', email_contents)\n",
    "\n",
    "    for token in email_contents:\n",
    "\n",
    "        # Remove any non alphanumeric characters\n",
    "        token = re.sub('[^a-zA-Z0-9]', '', token)\n",
    "\n",
    "        # Stem the word \n",
    "        token = PorterStemmer().stem_word(token.strip())\n",
    "\n",
    "        # Skip the word if it is too short\n",
    "        if len(token) < 1:\n",
    "           continue\n",
    "\n",
    "        # Look up the word in the dictionary and add to word_indices if found\n",
    "        idx = vocabList[token] if token in vocabList else 0\n",
    "\n",
    "        # only add entries which are in vocabList\n",
    "        #   i.e. those with ind ~= 0, \n",
    "        #        given that ind is assigned 0 if str is not found in vocabList\n",
    "        if idx > 0:\n",
    "            word_indices.append(idx)\n",
    "\n",
    "        # Print to screen, ensuring that the output lines are not too long\n",
    "        if verbose:\n",
    "            if l + len(token) + 1 > 78:\n",
    "                print(\"\")\n",
    "                l = 0\n",
    "            print('{:s}'.format(token)),\n",
    "            l = l + len(token) + 1\n",
    "\n",
    "    # Print footer\n",
    "    if verbose: print('\\n\\n=========================\\n')\n",
    "\n",
    "    return word_indices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the email before processing...\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> Anyone knows how much it costs to host a web portal ?\n",
      ">\n",
      "Well, it depends on how many visitors you're expecting.\n",
      "This can be anywhere from less than 10 bucks a month to a couple of $100. \n",
      "You should checkout http://www.rackspace.com/ or perhaps Amazon EC2 \n",
      "if youre running something big..\n",
      "\n",
      "To unsubscribe yourself from this mailing list, send an email to:\n",
      "groupname-unsubscribe@egroups.com\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "file_contents = readFile('notebooks/svm-files/emailSample1.txt')\n",
    "print(file_contents)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "...and after processing, where we end up with a list of words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Processed Email ====\n",
      "\n",
      "\n",
      "anyon\n",
      "know\n",
      "how\n",
      "much\n",
      "it\n",
      "cost\n",
      "to\n",
      "host\n",
      "a\n",
      "web\n",
      "portal\n",
      "well\n",
      "it\n",
      "depend\n",
      "on\n",
      "how\n",
      "mani\n",
      "\n",
      "visitor\n",
      "you\n",
      "re\n",
      "expect\n",
      "thi\n",
      "can\n",
      "be\n",
      "anywher\n",
      "from\n",
      "less\n",
      "than\n",
      "number\n",
      "buck\n",
      "a\n",
      "month\n",
      "\n",
      "to\n",
      "a\n",
      "coupl\n",
      "of\n",
      "dollarnumb\n",
      "you\n",
      "should\n",
      "checkout\n",
      "httpaddr\n",
      "or\n",
      "perhap\n",
      "amazon\n",
      "ecnumb\n",
      "\n",
      "if\n",
      "your\n",
      "run\n",
      "someth\n",
      "big\n",
      "to\n",
      "unsubscrib\n",
      "yourself\n",
      "from\n",
      "thi\n",
      "mail\n",
      "list\n",
      "send\n",
      "an\n",
      "\n",
      "email\n",
      "to\n",
      "emailaddr\n",
      "\n",
      "\n",
      "=========================\n",
      "\n",
      "Word Indices: \n",
      " [86, 916, 794, 1077, 883, 370, 1699, 790, 1822, 1831, 883, 431, 1171, 794, 1002, 1893, 1364, 592, 1676, 238, 162, 89, 688, 945, 1663, 1120, 1062, 1699, 375, 1162, 479, 1893, 1510, 799, 1182, 1237, 810, 1895, 1440, 1547, 181, 1699, 1758, 1896, 688, 1676, 992, 961, 1477, 71, 530, 1699, 531]\n"
     ]
    }
   ],
   "source": [
    "file_contents = readFile('notebooks/svm-files/emailSample1.txt')\n",
    "word_indices  = processEmail(file_contents)\n",
    "\n",
    "print('Word Indices: ')\n",
    "print(' {:s}'.format(word_indices))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature extraction\n",
    "\n",
    "From here, we can now turn emails into vectors in $\\mathbb{R}^{n}$ (vectors with $n$ terms or $n$ dimensions), where $n$ is the size of our vocabulary, 1899.\n",
    "\n",
    "Each vector derived from an email will represent the presence in the email (1) or absence from the email (0) of each of the words of the vocabulary.\n",
    "\n",
    "``emailFeatures()`` below extracts these features from emails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def emailFeatures(word_indices):\n",
    "    \"\"\"takes in a word_indices vector and produces a feature vector\n",
    "    from the word indices\"\"\"\n",
    "    n = 1899\n",
    "    x = np.zeros((n, 1))\n",
    "    for idx in word_indices:\n",
    "        x[idx] = 1\n",
    "    \n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turning the email above into a vector now consists of extracting its features! Below we can see how many elements of its feature vector are nonzero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of feature vector: 1899\n",
      "Number of non-zero entries: 45\n"
     ]
    }
   ],
   "source": [
    "file_contents = readFile('notebooks/svm-files/emailSample1.txt')\n",
    "word_indices  = processEmail(file_contents, verbose=False)\n",
    "features      = emailFeatures(word_indices)\n",
    "\n",
    "print('Length of feature vector: {:d}'.format( len(features) ) )\n",
    "print('Number of non-zero entries: {:d}'.format( np.sum(features > 0) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, 45 is also the number of unique word indices in the list resulting from email preprocessing.\n",
    "\n",
    "## Training a spam classifier\n",
    "\n",
    "With a pipeline from email to feature vector established, we can work with the (previously preprocessed) emails feature vectors in the ``spamTrain.mat`` file. \n",
    "\n",
    "With these email feature vectors we will train a SVM spam classifier model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Linear SVM Spam Classification (this may take 1 to 2 minutes)...\n",
      "[LibSVM]"
     ]
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('notebooks/svm-files/spamTrain.mat')\n",
    "X = mat[\"X\"]\n",
    "y = mat[\"y\"]\n",
    "\n",
    "print('Training Linear SVM Spam Classification (this may take 1 to 2 minutes)...')\n",
    "\n",
    "C = 0.1\n",
    "model = svmTrain(X, y, C, \"linear\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we make predictions on the training data from the model and assess their accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Accuracy: 99.825000\n"
     ]
    }
   ],
   "source": [
    "p = model.predict(X)\n",
    "print('Training Accuracy: {:f}'.format( np.mean((p == y.flatten()).astype(int)) * 100 ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we evaluate the model on unseen test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating the trained Linear SVM on a test set ...\n",
      "Test Accuracy: 98.900000\n"
     ]
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('notebooks/svm-files/spamTest.mat')\n",
    "Xtest = mat[\"Xtest\"]\n",
    "ytest = mat[\"ytest\"]\n",
    "\n",
    "print('Evaluating the trained Linear SVM on a test set ...')\n",
    "\n",
    "p = model.predict(Xtest)\n",
    "print('Test Accuracy: {:f}'.format( np.mean((p == ytest.flatten()).astype(int)) * 100 ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding a spam classifier\n",
    "\n",
    "One advantage of using the linear kernel for our SVM is that we can peek inside the weights to better understand how it discriminates spam from non-spam (ham?) email.\n",
    "\n",
    "The following are the words that the classifier has most strongly linked to a positive spam classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Top predictors of spam: \n",
      "\n",
      " our (0.500614) \n",
      " click (0.465916) \n",
      " remov (0.422869) \n",
      " guarante (0.383622) \n",
      " visit (0.367710) \n",
      " basenumb (0.345064) \n",
      " dollar (0.323632) \n",
      " will (0.269724) \n",
      " price (0.267298) \n",
      " pleas (0.261169) \n",
      " most (0.257298) \n",
      " nbsp (0.253941) \n",
      " lo (0.253467) \n",
      " ga (0.248297) \n",
      " hour (0.246404) \n"
     ]
    }
   ],
   "source": [
    "w = model.coef_[0]\n",
    "indices = w.argsort()[::-1][:15]\n",
    "vocabList = sorted(getVocabList().keys())\n",
    "\n",
    "print('\\nTop predictors of spam: \\n');\n",
    "for idx in indices: \n",
    "    print( ' {:s} ({:f}) '.format( vocabList[idx], float(w[idx]) ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More spam! (Maybe!)\n",
    "\n",
    "Since we established a pipeline to process emails to determine whether they're spam or not, it makes sense to use it for at least a few more examples.\n",
    "\n",
    "Below we read a few normal and spam emails and show how the model classifies them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Processed notebooks/svm-files/spamSample1.txt\n",
      "\n",
      "Spam Classification: [0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "filename = 'notebooks/svm-files/spamSample1.txt'\n",
    "\n",
    "# Read and predict\n",
    "file_contents = readFile(filename)\n",
    "word_indices  = processEmail(file_contents, verbose=False)\n",
    "x             = emailFeatures(word_indices)\n",
    "p = model.predict(x.reshape(1, -1))\n",
    "\n",
    "print('\\nProcessed {:s}\\n\\nSpam Classification: {:s}\\n'.format(filename, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oops! 💩"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Processed notebooks/svm-files/spamSample2.txt\n",
      "\n",
      "Spam Classification: [1]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "filename = 'notebooks/svm-files/spamSample2.txt'\n",
    "\n",
    "# Read and predict\n",
    "file_contents = readFile(filename)\n",
    "word_indices  = processEmail(file_contents, verbose=False)\n",
    "x             = emailFeatures(word_indices)\n",
    "p = model.predict(x.reshape(1, -1))\n",
    "\n",
    "print('\\nProcessed {:s}\\n\\nSpam Classification: {:s}\\n'.format(filename, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "🙌"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Processed notebooks/svm-files/emailSample1.txt\n",
      "\n",
      "Spam Classification: [0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "filename = 'notebooks/svm-files/emailSample1.txt'\n",
    "\n",
    "# Read and predict\n",
    "file_contents = readFile(filename)\n",
    "word_indices  = processEmail(file_contents, verbose=False)\n",
    "x             = emailFeatures(word_indices)\n",
    "p = model.predict(x.reshape(1, -1))\n",
    "\n",
    "print('\\nProcessed {:s}\\n\\nSpam Classification: {:s}\\n'.format(filename, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "👍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Processed notebooks/svm-files/emailSample2.txt\n",
      "\n",
      "Spam Classification: [0]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "filename = 'notebooks/svm-files/emailSample2.txt'\n",
    "\n",
    "# Read and predict\n",
    "file_contents = readFile(filename)\n",
    "word_indices  = processEmail(file_contents, verbose=False)\n",
    "x             = emailFeatures(word_indices)\n",
    "p = model.predict(x.reshape(1, -1))\n",
    "\n",
    "print('\\nProcessed {:s}\\n\\nSpam Classification: {:s}\\n'.format(filename, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "👏"
   ]
  }
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