1471 lines
401 KiB
Plaintext
1471 lines
401 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h1> Programming Exercise 6: Support Vector Machines</h1>\n",
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"<h3> Introduction </h3>\n",
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"In this exercise, we will use support vector machines (SVMs) to build a spam classifier. To start we will import necessary libraries."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"metadata": {},
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"outputs": [],
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"source": [
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"# used for manipulating directory paths\n",
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"import os\n",
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"\n",
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"# Scientific and vector computation for python\n",
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"import numpy as np\n",
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"\n",
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"# Import regular expressions to process emails\n",
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"import re\n",
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"\n",
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"# Plotting library\n",
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"from matplotlib import pyplot as plt\n",
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"\n",
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"# Optimization module in scipy\n",
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"from scipy import optimize\n",
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"\n",
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"# will be used to load MATLAB mat datafile format\n",
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"from scipy.io import loadmat\n",
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"\n",
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"# tells matplotlib to embed plots within the notebook\n",
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"%matplotlib inline\n",
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"\n",
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"from os.path import join"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h3> 1 Support Vector Machines</h3>\n",
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"In the first half of this exercise, we will be using SVMs with various 2d datasets. Experimenting with these datasets can reveal how SVMs work and show us how to use a gaussian kernel with SVMs.\n",
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"\n",
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"<h3>1.1 Example Dataset 1</h3>\n",
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"We begin with a 2D example dataset which can be seperated by a linear boundary. We will plot the data into a figure where positive samples are represented with an x and negative samples with an o. Notice there is an outlier positive sample. We will see how this affects our SVM decision boundary. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 46,
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"metadata": {},
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"outputs": [],
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"source": [
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"def plotData(X, y, grid=False):\n",
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" \"\"\"\n",
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" Plots the data points X and y into a new figure. Uses `+` for positive examples, and `o` for\n",
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" negative examples. `X` is assumed to be a Mx2 matrix\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" X : numpy ndarray\n",
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" X is assumed to be a Mx2 matrix.\n",
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"\n",
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" y : numpy ndarray\n",
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" The data labels.\n",
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"\n",
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" grid : bool (Optional)\n",
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" Specify whether or not to show the grid in the plot. It is False by default.\n",
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"\n",
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" Notes\n",
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" -----\n",
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" This was slightly modified such that it expects y=1 or y=0.\n",
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" \"\"\"\n",
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" # Find Indices of Positive and Negative Examples\n",
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" pos = y == 1\n",
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" neg = y == 0\n",
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"\n",
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" # Plot Examples\n",
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" plt.plot(X[pos, 0], X[pos, 1], 'X', mew=1, ms=10, mec='k')\n",
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" plt.plot(X[neg, 0], X[neg, 1], 'o', mew=1, mfc='y', ms=10, mec='k')\n",
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" plt.grid(grid)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 47,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
|
|
"text/plain": [
|
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"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load from ex6data1\n",
|
|
"# You will have X, y as keys in the dict data\n",
|
|
"data = loadmat(os.path.join('Data', 'ex6data1.mat'))\n",
|
|
"X, y = data['X'], data['y'][:, 0]\n",
|
|
"\n",
|
|
"# Plot training data\n",
|
|
"plotData(X, y)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"In this part of the exercise, we will try using different values of the C paremeter with SVMs. Informally, the C parameter is a positive value that controls the penalty for misclassified training samples. A large C tells the SVM to classify all samples correctly. C plays a role similar to 1/(lambda) where lambda is the regularization parameter used in logistic regression.\n",
|
|
"<table style=\"text-align:center\">\n",
|
|
" <tr>\n",
|
|
" <th colspan=\"2\" style=\"text-align:center\">SVM Decision boundary for example dataset 1 </th>\n",
|
|
" </tr>\n",
|
|
" <tr>\n",
|
|
" <td style=\"text-align:center\">C=1<img src=\"Figures/svm_c1.png\"/></td>\n",
|
|
" <td style=\"text-align:center\">C=100<img src=\"Figures/svm_c100.png\"/></td>\n",
|
|
" </tr>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"To see the impacts more directly, you can vary C in the following code and run the SVM training again. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 48,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def svmTrain(X, Y, C, kernelFunction, tol=1e-3, max_passes=5, args=()):\n",
|
|
" \"\"\"\n",
|
|
" Trains an SVM classifier using a simplified version of the SMO algorithm.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ---------\n",
|
|
" X : numpy ndarray\n",
|
|
" (m x n) Matrix of training examples. Each row is a training example, and the\n",
|
|
" jth column holds the jth feature.\n",
|
|
"\n",
|
|
" Y : numpy ndarray\n",
|
|
" (m, ) A vector (1-D numpy array) containing 1 for positive examples and 0 for negative examples.\n",
|
|
"\n",
|
|
" C : float\n",
|
|
" The standard SVM regularization parameter.\n",
|
|
"\n",
|
|
" kernelFunction : func\n",
|
|
" A function handle which computes the kernel. The function should accept two vectors as\n",
|
|
" inputs, and returns a scalar as output.\n",
|
|
"\n",
|
|
" tol : float, optional\n",
|
|
" Tolerance value used for determining equality of floating point numbers.\n",
|
|
"\n",
|
|
" max_passes : int, optional\n",
|
|
" Controls the number of iterations over the dataset (without changes to alpha)\n",
|
|
" before the algorithm quits.\n",
|
|
"\n",
|
|
" args : tuple\n",
|
|
" Extra arguments required for the kernel function, such as the sigma parameter for a\n",
|
|
" Gaussian kernel.\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" model :\n",
|
|
" The trained SVM model.\n",
|
|
"\n",
|
|
" Notes\n",
|
|
" -----\n",
|
|
" This is a simplified version of the SMO algorithm for training SVMs. In practice, if\n",
|
|
" you want to train an SVM classifier, we recommend using an optimized package such as:\n",
|
|
"\n",
|
|
" - LIBSVM (http://www.csie.ntu.edu.tw/~cjlin/libsvm/)\n",
|
|
" - SVMLight (http://svmlight.joachims.org/)\n",
|
|
" - scikit-learn (http://scikit-learn.org/stable/modules/svm.html) which contains python wrappers\n",
|
|
" for the LIBSVM library.\n",
|
|
" \"\"\"\n",
|
|
" # make sure data is signed int\n",
|
|
" Y = Y.astype(int)\n",
|
|
" # Dataset size parameters\n",
|
|
" m, n = X.shape\n",
|
|
"\n",
|
|
" passes = 0\n",
|
|
" E = np.zeros(m)\n",
|
|
" alphas = np.zeros(m)\n",
|
|
" b = 0\n",
|
|
"\n",
|
|
" # Map 0 to -1\n",
|
|
" Y[Y == 0] = -1\n",
|
|
"\n",
|
|
" # Pre-compute the Kernel Matrix since our dataset is small\n",
|
|
" # (in practice, optimized SVM packages that handle large datasets\n",
|
|
" # gracefully will **not** do this)\n",
|
|
"\n",
|
|
" # We have implemented the optimized vectorized version of the Kernels here so\n",
|
|
" # that the SVM training will run faster\n",
|
|
" if kernelFunction.__name__ == 'linearKernel':\n",
|
|
" # Vectorized computation for the linear kernel\n",
|
|
" # This is equivalent to computing the kernel on every pair of examples\n",
|
|
" K = np.dot(X, X.T)\n",
|
|
" elif kernelFunction.__name__ == 'gaussianKernel':\n",
|
|
" # vectorized RBF Kernel\n",
|
|
" # This is equivalent to computing the kernel on every pair of examples\n",
|
|
" X2 = np.sum(X**2, axis=1)\n",
|
|
" K = X2 + X2[:, None] - 2 * np.dot(X, X.T)\n",
|
|
"\n",
|
|
" if len(args) > 0:\n",
|
|
" K /= 2*args[0]**2\n",
|
|
"\n",
|
|
" K = np.exp(-K)\n",
|
|
" else:\n",
|
|
" K = np.zeros((m, m))\n",
|
|
" for i in range(m):\n",
|
|
" for j in range(i, m):\n",
|
|
" K[i, j] = kernelFunction(X[i, :], X[j, :])\n",
|
|
" K[j, i] = K[i, j]\n",
|
|
"\n",
|
|
" while passes < max_passes:\n",
|
|
" num_changed_alphas = 0\n",
|
|
" for i in range(m):\n",
|
|
" E[i] = b + np.sum(alphas * Y * K[:, i]) - Y[i]\n",
|
|
"\n",
|
|
" if (Y[i]*E[i] < -tol and alphas[i] < C) or (Y[i]*E[i] > tol and alphas[i] > 0):\n",
|
|
" # select the alpha_j randomly\n",
|
|
" j = np.random.choice(list(range(i)) + list(range(i+1, m)), size=1)[0]\n",
|
|
"\n",
|
|
" E[j] = b + np.sum(alphas * Y * K[:, j]) - Y[j]\n",
|
|
"\n",
|
|
" alpha_i_old = alphas[i]\n",
|
|
" alpha_j_old = alphas[j]\n",
|
|
"\n",
|
|
" if Y[i] == Y[j]:\n",
|
|
" L = max(0, alphas[j] + alphas[i] - C)\n",
|
|
" H = min(C, alphas[j] + alphas[i])\n",
|
|
" else:\n",
|
|
" L = max(0, alphas[j] - alphas[i])\n",
|
|
" H = min(C, C + alphas[j] - alphas[i])\n",
|
|
"\n",
|
|
" if L == H:\n",
|
|
" continue\n",
|
|
"\n",
|
|
" eta = 2 * K[i, j] - K[i, i] - K[j, j]\n",
|
|
"\n",
|
|
" # objective function positive definite, there will be a minimum along the direction\n",
|
|
" # of linear equality constrain, and eta will be greater than zero\n",
|
|
" # we are actually computing -eta here (so we skip of eta >= 0)\n",
|
|
" if eta >= 0:\n",
|
|
" continue\n",
|
|
"\n",
|
|
" alphas[j] -= Y[j] * (E[i] - E[j])/eta\n",
|
|
" alphas[j] = max(L, min(H, alphas[j]))\n",
|
|
"\n",
|
|
" if abs(alphas[j] - alpha_j_old) < tol:\n",
|
|
" alphas[j] = alpha_j_old\n",
|
|
" continue\n",
|
|
" alphas[i] += Y[i]*Y[j]*(alpha_j_old - alphas[j])\n",
|
|
"\n",
|
|
" b1 = b - E[i] - Y[i]*(alphas[i] - alpha_i_old) * K[i, j] \\\n",
|
|
" - Y[j] * (alphas[j] - alpha_j_old) * K[i, j]\n",
|
|
"\n",
|
|
" b2 = b - E[j] - Y[i]*(alphas[i] - alpha_i_old) * K[i, j] \\\n",
|
|
" - Y[j] * (alphas[j] - alpha_j_old) * K[j, j]\n",
|
|
"\n",
|
|
" if 0 < alphas[i] < C:\n",
|
|
" b = b1\n",
|
|
" elif 0 < alphas[j] < C:\n",
|
|
" b = b2\n",
|
|
" else:\n",
|
|
" b = (b1 + b2)/2\n",
|
|
"\n",
|
|
" num_changed_alphas += 1\n",
|
|
" if num_changed_alphas == 0:\n",
|
|
" passes += 1\n",
|
|
" else:\n",
|
|
" passes = 0\n",
|
|
"\n",
|
|
" idx = alphas > 0\n",
|
|
" model = {'X': X[idx, :],\n",
|
|
" 'y': Y[idx],\n",
|
|
" 'kernelFunction': kernelFunction,\n",
|
|
" 'b': b,\n",
|
|
" 'args': args,\n",
|
|
" 'alphas': alphas[idx],\n",
|
|
" 'w': np.dot(alphas * Y, X)}\n",
|
|
" return model"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 49,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def linearKernel(x1, x2):\n",
|
|
" \"\"\"\n",
|
|
" Returns a linear kernel between x1 and x2.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" x1 : numpy ndarray\n",
|
|
" A 1-D vector.\n",
|
|
"\n",
|
|
" x2 : numpy ndarray\n",
|
|
" A 1-D vector of same size as x1.\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" : float\n",
|
|
" The scalar amplitude.\n",
|
|
" \"\"\"\n",
|
|
" return np.dot(x1, x2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 50,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def visualizeBoundaryLinear(X, y, model):\n",
|
|
" \"\"\"\n",
|
|
" Plots a linear decision boundary learned by the SVM.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" X : array_like\n",
|
|
" (m x 2) The training data with two features (to plot in a 2-D plane).\n",
|
|
"\n",
|
|
" y : array_like\n",
|
|
" (m, ) The data labels.\n",
|
|
"\n",
|
|
" model : dict\n",
|
|
" Dictionary of model variables learned by SVM.\n",
|
|
" \"\"\"\n",
|
|
" w, b = model['w'], model['b']\n",
|
|
" xp = np.linspace(min(X[:, 0]), max(X[:, 0]), 100)\n",
|
|
" yp = -(w[0] * xp + b)/w[1]\n",
|
|
"\n",
|
|
" plotData(X, y)\n",
|
|
" plt.plot(xp, yp, '-b')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 51,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# You should try to change the C value below and see how the decision\n",
|
|
"# boundary varies (e.g., try C = 1000)\n",
|
|
"C = 1\n",
|
|
"\n",
|
|
"model = svmTrain(X, y, C, linearKernel, 1e-3, 20)\n",
|
|
"visualizeBoundaryLinear(X, y, model)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h4>1.2 SVM with Gaussian Kernals</h4>\n",
|
|
"In this part of the exercise, we will be using SVMs to do non-linear classification. To find non-linear decision boundaries with the SVM, we need to first implement a Gaussian kernel. A Gaussian kernal can be throught of as a similarity function that measures the \"distance\" between pairs of examples. The kernel is also parameterized by a bandwidth parameter sigma which determines how fast the similarity metric decreases as examples are further apart. We now create a function to compute the Gaussian kernel between to examples. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 52,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def gaussianKernel(x1, x2, sigma):\n",
|
|
" \"\"\"\n",
|
|
" Computes the radial basis function\n",
|
|
" Returns a radial basis function kernel between x1 and x2.\n",
|
|
" \n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" x1 : numpy ndarray\n",
|
|
" A vector of size (n, ), representing the first datapoint.\n",
|
|
" \n",
|
|
" x2 : numpy ndarray\n",
|
|
" A vector of size (n, ), representing the second datapoint.\n",
|
|
" \n",
|
|
" sigma : float\n",
|
|
" The bandwidth parameter for the Gaussian kernel.\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" sim : float\n",
|
|
" The computed RBF between the two provided data points.\n",
|
|
" \"\"\"\n",
|
|
" sim = 0\n",
|
|
" temp = np.square(x1-x2)\n",
|
|
" temp = np.sum(temp)\n",
|
|
" temp = temp * (-1)\n",
|
|
" temp = temp / (2 * (sigma**2))\n",
|
|
" sim = np.exp(temp)\n",
|
|
"\n",
|
|
" return sim"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We will now load and plot dataset 2."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 53,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load from ex6data2\n",
|
|
"# You will have X, y as keys in the dict data\n",
|
|
"data = loadmat(os.path.join('Data', 'ex6data2.mat'))\n",
|
|
"X, y = data['X'], data['y'][:, 0]\n",
|
|
"\n",
|
|
"# Plot training data\n",
|
|
"plotData(X, y)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"From this figure we can observe that there is no linear decision boundary which could seperate the positive and negative examples for this dataset. However, by using the Gaussian kernal with the SVM, we will be able to learn a non-linear decision boundary that can perform reasonably well."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 54,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def visualizeBoundary(X, y, model):\n",
|
|
" \"\"\"\n",
|
|
" Plots a non-linear decision boundary learned by the SVM and overlays the data on it.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" X : array_like\n",
|
|
" (m x 2) The training data with two features (to plot in a 2-D plane).\n",
|
|
"\n",
|
|
" y : array_like\n",
|
|
" (m, ) The data labels.\n",
|
|
"\n",
|
|
" model : dict\n",
|
|
" Dictionary of model variables learned by SVM.\n",
|
|
" \"\"\"\n",
|
|
" plotData(X, y)\n",
|
|
"\n",
|
|
" # make classification predictions over a grid of values\n",
|
|
" x1plot = np.linspace(min(X[:, 0]), max(X[:, 0]), 100)\n",
|
|
" x2plot = np.linspace(min(X[:, 1]), max(X[:, 1]), 100)\n",
|
|
" X1, X2 = np.meshgrid(x1plot, x2plot)\n",
|
|
"\n",
|
|
" vals = np.zeros(X1.shape)\n",
|
|
" for i in range(X1.shape[1]):\n",
|
|
" this_X = np.stack((X1[:, i], X2[:, i]), axis=1)\n",
|
|
" vals[:, i] = svmPredict(model, this_X)\n",
|
|
"\n",
|
|
" plt.contour(X1, X2, vals, colors='y', linewidths=2)\n",
|
|
" plt.pcolormesh(X1, X2, vals, cmap='YlGnBu', alpha=0.25, edgecolors='None', lw=0)\n",
|
|
" plt.grid(False)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 55,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# SVM Parameters\n",
|
|
"C = 1\n",
|
|
"sigma = 0.1\n",
|
|
"\n",
|
|
"model= svmTrain(X, y, C, gaussianKernel, args=(sigma,))\n",
|
|
"visualizeBoundary(X, y, model)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We will now gain more practical skills on how to use an SVM with a Gaussian kernel. We begin by loading and displaying the third dataset."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 56,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load from ex6data3\n",
|
|
"# You will have X, y, Xval, yval as keys in the dict data\n",
|
|
"data = loadmat(os.path.join('Data', 'ex6data3.mat'))\n",
|
|
"X, y, Xval, yval = data['X'], data['y'][:, 0], data['Xval'], data['yval'][:, 0]\n",
|
|
"\n",
|
|
"# Plot training data\n",
|
|
"plotData(X, y)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"In this dataset we have the variables X, y, Xval, yval. Our task is to use the cross validation set Xval, yval to determine the best C and sigma parameters to use for our decision boundary."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 57,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def dataset3Params(X, y, Xval, yval):\n",
|
|
" \"\"\"\n",
|
|
" Returns your choice of C and sigma for Part 3 of the exercise \n",
|
|
" where you select the optimal (C, sigma) learning parameters to use for SVM\n",
|
|
" with RBF kernel.\n",
|
|
" \n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" X : array_like\n",
|
|
" (m x n) matrix of training data where m is number of training examples, and \n",
|
|
" n is the number of features.\n",
|
|
" \n",
|
|
" y : array_like\n",
|
|
" (m, ) vector of labels for ther training data.\n",
|
|
" \n",
|
|
" Xval : array_like\n",
|
|
" (mv x n) matrix of validation data where mv is the number of validation examples\n",
|
|
" and n is the number of features\n",
|
|
" \n",
|
|
" yval : array_like\n",
|
|
" (mv, ) vector of labels for the validation data.\n",
|
|
" \n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" C, sigma : float, float\n",
|
|
" The best performing values for the regularization parameter C and \n",
|
|
" RBF parameter sigma.\n",
|
|
" \"\"\"\n",
|
|
" C = 1\n",
|
|
" sigma = 0.3\n",
|
|
"\n",
|
|
" sampleVec = np.array([.01, .03, .1, .3, 1, 3, 10, 30])\n",
|
|
" model= svmTrain(X, y, C, gaussianKernel, args=(sigma,))\n",
|
|
" predictions = svmPredict(model, Xval)\n",
|
|
" error = np.mean(predictions != yval)\n",
|
|
" for i in range(8):\n",
|
|
" for j in range(8):\n",
|
|
" tempC = sampleVec[i]\n",
|
|
" tempSigma = sampleVec[j]\n",
|
|
" tempModel = svmTrain(X, y, tempC, gaussianKernel, args=(tempSigma,))\n",
|
|
" tempPredictions = svmPredict(tempModel, Xval)\n",
|
|
" tempError = np.mean(tempPredictions != yval)\n",
|
|
" if tempError < error:\n",
|
|
" error = tempError\n",
|
|
" C = tempC\n",
|
|
" sigma = tempSigma\n",
|
|
"\n",
|
|
" return C, sigma"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 58,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"1.0 0.1\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Try different SVM Parameters here\n",
|
|
"C, sigma = dataset3Params(X, y, Xval, yval)\n",
|
|
"\n",
|
|
"# Train the SVM\n",
|
|
"# model = utils.svmTrain(X, y, C, lambda x1, x2: gaussianKernel(x1, x2, sigma))\n",
|
|
"model = svmTrain(X, y, C, gaussianKernel, args=(sigma,))\n",
|
|
"visualizeBoundary(X, y, model)\n",
|
|
"print(C, sigma)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h3> 2 Spam Classification</h3>\n",
|
|
"Many email services today provide spam filters which are able to classify emails into spam and non-spam email with high accuracy. In this part of the exercise, we will use SVMs to build our own spam filter.\n",
|
|
"\n",
|
|
"We will be training a classifier to classify whether a given email, x, is spam (y=1) or non-spam (y=0). In particular we need to convert each email into an n-dimensional feature vector.\n",
|
|
"\n",
|
|
"<h4>2.1 Preprocessing Emails</h4>\n",
|
|
"Before starting on a machine learning task, it is usually insightful to take a look at examples from the dataset. the following figure shows a sample email which contains a URL, email addess, numbers, and dollar amounts. While many emails would contain similar types of entitiers, the specific entities will be different in almost every email. Therefore, one method often employed in processing emails is to \"normalize\" these values, so that all URLs are treated the same, all numbers the same, etc. For examplem we could replace each URL with the unique string \"httppadr\" to indicate a URL was present. \n",
|
|
"\n",
|
|
"This has the effect of letting the spam classifier make a classification decision based on whether any URL was present as opposed to a specific URL. in processEmail we have implemented the following steps:\n",
|
|
"- **Lower-casing**: The entire email is converted into lower case, so that captialization is ignored (e.g., IndIcaTE is treated the same as Indicate).\n",
|
|
"\n",
|
|
"- **Stripping HTML**: All HTML tags are removed from the emails. Many emails often come with HTML formatting; we remove all the HTML tags, so that only the content remains.\n",
|
|
"\n",
|
|
"- **Normalizing URLs**: All URLs are replaced with the text “httpaddr”.\n",
|
|
"\n",
|
|
"- **Normalizing Email Addresses**: All email addresses are replaced with the text “emailaddr”.\n",
|
|
"\n",
|
|
"- **Normalizing Numbers**: All numbers are replaced with the text “number”.\n",
|
|
"\n",
|
|
"- **Normalizing Dollars**: All dollar signs ($) are replaced with the text “dollar”.\n",
|
|
"\n",
|
|
"- **Word Stemming**: Words are reduced to their stemmed form. For example, “discount”, “discounts”, “discounted” and “discounting” are all replaced with “discount”. Sometimes, the Stemmer actually strips off additional characters from the end, so “include”, “includes”, “included”, and “including” are all replaced with “includ”.\n",
|
|
"\n",
|
|
"- **Removal of non-words**: Non-words and punctuation have been removed. All white spaces (tabs, newlines, spaces) have all been trimmed to a single space character.\n",
|
|
"\n",
|
|
"<img src=\"Figures/email.png\" width=\"700px\" />\n",
|
|
"\n",
|
|
"The result of these preprocessing steps is shown in the figure below. \n",
|
|
"\n",
|
|
"<img src=\"Figures/email_cleaned.png\" alt=\"email cleaned\" style=\"width: 600px;\"/>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"After preprocessing the emails, we have a list of words for each email. The next step is to choose which words we would like to use in our classifier and which we would want to leave out.\n",
|
|
"\n",
|
|
"For this exercise, we have chosen only the most frequently occuring words as our set of words considered (the vocabulary list). Since words that occur rarely in the training set are only in a few emails, they might cause the\n",
|
|
"model to overfit our training set. The complete vocabulary list is in the file `vocab.txt` (inside the `Data` directory for this exercise) and also shown in the figure below.\n",
|
|
"\n",
|
|
"<img src=\"Figures/vocab.png\" alt=\"Vocab\" width=\"150px\" />\n",
|
|
"\n",
|
|
"Our vocabulary list was selected by choosing all words which occur at least a 100 times in the spam corpus,\n",
|
|
"resulting in a list of 1899 words. In practice, a vocabulary list with about 10,000 to 50,000 words is often used.\n",
|
|
"Given the vocabulary list, we can now map each word in the preprocessed emails into a list of word indices that contains the index of the word in the vocabulary dictionary. The figure below shows the mapping for the sample email. Specifically, in the sample email, the word “anyone” was first normalized to “anyon” and then mapped onto the index 86 in the vocabulary list.\n",
|
|
"\n",
|
|
"<img src=\"Figures/word_indices.png\" alt=\"word indices\" width=\"200px\" />\n",
|
|
"\n",
|
|
"Our task now is to complete the code in the function `processEmail` to perform this mapping. In the code, we have a string `word` which is a single word from the processed email. We need to look up the word in the vocabulary list `vocabList`. If the word exists in the list, we will add the index of the word into the `word_indices` variable. If the word does not exist, and is therefore not in the vocabulary, we will skip the word.\n",
|
|
"\n",
|
|
"<a id=\"processEmail\"></a>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 59,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getVocabList():\n",
|
|
" \"\"\"\n",
|
|
" Reads the fixed vocabulary list in vocab.txt and returns a cell array of the words\n",
|
|
" % vocabList = GETVOCABLIST() reads the fixed vocabulary list in vocab.txt\n",
|
|
" % and returns a cell array of the words in vocabList.\n",
|
|
"\n",
|
|
" :return:\n",
|
|
" \"\"\"\n",
|
|
" vocabList = np.genfromtxt(join('Data', 'vocab.txt'), dtype=object)\n",
|
|
" return list(vocabList[:, 1].astype(str))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 60,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"class PorterStemmer:\n",
|
|
" \"\"\"\n",
|
|
" Porter Stemming Algorithm\n",
|
|
"\n",
|
|
" This is the Porter stemming algorithm, ported to Python from the\n",
|
|
" version coded up in ANSI C by the author. It may be be regarded\n",
|
|
" as canonical, in that it follows the algorithm presented in\n",
|
|
"\n",
|
|
" Porter, 1980, An algorithm for suffix stripping, Program, Vol. 14,\n",
|
|
" no. 3, pp 130-137,\n",
|
|
"\n",
|
|
" only differing from it at the points maked --DEPARTURE-- below.\n",
|
|
"\n",
|
|
" See also http://www.tartarus.org/~martin/PorterStemmer\n",
|
|
"\n",
|
|
" The algorithm as described in the paper could be exactly replicated\n",
|
|
" by adjusting the points of DEPARTURE, but this is barely necessary,\n",
|
|
" because (a) the points of DEPARTURE are definitely improvements, and\n",
|
|
" (b) no encoding of the Porter stemmer I have seen is anything like\n",
|
|
" as exact as this version, even with the points of DEPARTURE!\n",
|
|
"\n",
|
|
" Vivake Gupta (v@nano.com)\n",
|
|
"\n",
|
|
" Release 1: January 2001\n",
|
|
"\n",
|
|
" Further adjustments by Santiago Bruno (bananabruno@gmail.com)\n",
|
|
" to allow word input not restricted to one word per line, leading\n",
|
|
" to:\n",
|
|
"\n",
|
|
" release 2: July 2008\n",
|
|
" \"\"\"\n",
|
|
" def __init__(self):\n",
|
|
" \"\"\"\n",
|
|
" The main part of the stemming algorithm starts here.\n",
|
|
" b is a buffer holding a word to be stemmed. The letters are in b[k0],\n",
|
|
" b[k0+1] ... ending at b[k]. In fact k0 = 0 in this demo program. k is\n",
|
|
" readjusted downwards as the stemming progresses. Zero termination is\n",
|
|
" not in fact used in the algorithm.\n",
|
|
"\n",
|
|
" Note that only lower case sequences are stemmed. Forcing to lower case\n",
|
|
" should be done before stem(...) is called.\n",
|
|
" \"\"\"\n",
|
|
" self.b = \"\" # buffer for word to be stemmed\n",
|
|
" self.k = 0\n",
|
|
" self.k0 = 0\n",
|
|
" self.j = 0 # j is a general offset into the string\n",
|
|
"\n",
|
|
" def cons(self, i):\n",
|
|
" \"\"\"cons(i) is TRUE <=> b[i] is a consonant.\"\"\"\n",
|
|
" if self.b[i] in 'aeiou':\n",
|
|
" return 0\n",
|
|
" if self.b[i] == 'y':\n",
|
|
" if i == self.k0:\n",
|
|
" return 1\n",
|
|
" else:\n",
|
|
" return not self.cons(i - 1)\n",
|
|
" return 1\n",
|
|
"\n",
|
|
" def m(self):\n",
|
|
" \"\"\"\n",
|
|
" m() measures the number of consonant sequences between k0 and j.\n",
|
|
" if c is a consonant sequence and v a vowel sequence, and <..>\n",
|
|
" indicates arbitrary presence,\n",
|
|
"\n",
|
|
" <c><v> gives 0\n",
|
|
" <c>vc<v> gives 1\n",
|
|
" <c>vcvc<v> gives 2\n",
|
|
" <c>vcvcvc<v> gives 3\n",
|
|
" ....\n",
|
|
" \"\"\"\n",
|
|
" n = 0\n",
|
|
" i = self.k0\n",
|
|
" while 1:\n",
|
|
" if i > self.j:\n",
|
|
" return n\n",
|
|
" if not self.cons(i):\n",
|
|
" break\n",
|
|
" i = i + 1\n",
|
|
" i = i + 1\n",
|
|
" while 1:\n",
|
|
" while 1:\n",
|
|
" if i > self.j:\n",
|
|
" return n\n",
|
|
" if self.cons(i):\n",
|
|
" break\n",
|
|
" i = i + 1\n",
|
|
" i = i + 1\n",
|
|
" n = n + 1\n",
|
|
" while 1:\n",
|
|
" if i > self.j:\n",
|
|
" return n\n",
|
|
" if not self.cons(i):\n",
|
|
" break\n",
|
|
" i = i + 1\n",
|
|
" i = i + 1\n",
|
|
"\n",
|
|
" def vowelinstem(self):\n",
|
|
" \"\"\"vowelinstem() is TRUE <=> k0,...j contains a vowel\"\"\"\n",
|
|
" for i in range(self.k0, self.j + 1):\n",
|
|
" if not self.cons(i):\n",
|
|
" return 1\n",
|
|
" return 0\n",
|
|
"\n",
|
|
" def doublec(self, j):\n",
|
|
" \"\"\" doublec(j) is TRUE <=> j,(j-1) contain a double consonant. \"\"\"\n",
|
|
" if j < (self.k0 + 1):\n",
|
|
" return 0\n",
|
|
" if self.b[j] != self.b[j-1]:\n",
|
|
" return 0\n",
|
|
" return self.cons(j)\n",
|
|
"\n",
|
|
" def cvc(self, i):\n",
|
|
" \"\"\"\n",
|
|
" cvc(i) is TRUE <=> i-2,i-1,i has the form consonant - vowel - consonant\n",
|
|
" and also if the second c is not w,x or y. this is used when trying to\n",
|
|
" restore an e at the end of a short e.g.\n",
|
|
"\n",
|
|
" cav(e), lov(e), hop(e), crim(e), but\n",
|
|
" snow, box, tray.\n",
|
|
" \"\"\"\n",
|
|
" if i < (self.k0 + 2) or not self.cons(i) or self.cons(i-1) or not self.cons(i-2):\n",
|
|
" return 0\n",
|
|
" ch = self.b[i]\n",
|
|
" if ch in 'wxy':\n",
|
|
" return 0\n",
|
|
" return 1\n",
|
|
"\n",
|
|
" def ends(self, s):\n",
|
|
" \"\"\"ends(s) is TRUE <=> k0,...k ends with the string s.\"\"\"\n",
|
|
" length = len(s)\n",
|
|
" if s[length - 1] != self.b[self.k]: # tiny speed-up\n",
|
|
" return 0\n",
|
|
" if length > (self.k - self.k0 + 1):\n",
|
|
" return 0\n",
|
|
" if self.b[self.k-length+1:self.k+1] != s:\n",
|
|
" return 0\n",
|
|
" self.j = self.k - length\n",
|
|
" return 1\n",
|
|
"\n",
|
|
" def setto(self, s):\n",
|
|
" \"\"\"setto(s) sets (j+1),...k to the characters in the string s, readjusting k.\"\"\"\n",
|
|
" length = len(s)\n",
|
|
" self.b = self.b[:self.j+1] + s + self.b[self.j+length+1:]\n",
|
|
" self.k = self.j + length\n",
|
|
"\n",
|
|
" def r(self, s):\n",
|
|
" \"\"\"r(s) is used further down.\"\"\"\n",
|
|
" if self.m() > 0:\n",
|
|
" self.setto(s)\n",
|
|
"\n",
|
|
" def step1ab(self):\n",
|
|
" \"\"\"step1ab() gets rid of plurals and -ed or -ing. e.g.\n",
|
|
"\n",
|
|
" caresses -> caress\n",
|
|
" ponies -> poni\n",
|
|
" ties -> ti\n",
|
|
" caress -> caress\n",
|
|
" cats -> cat\n",
|
|
"\n",
|
|
" feed -> feed\n",
|
|
" agreed -> agree\n",
|
|
" disabled -> disable\n",
|
|
"\n",
|
|
" matting -> mat\n",
|
|
" mating -> mate\n",
|
|
" meeting -> meet\n",
|
|
" milling -> mill\n",
|
|
" messing -> mess\n",
|
|
"\n",
|
|
" meetings -> meet\n",
|
|
" \"\"\"\n",
|
|
" if self.b[self.k] == 's':\n",
|
|
" if self.ends(\"sses\"):\n",
|
|
" self.k = self.k - 2\n",
|
|
" elif self.ends(\"ies\"):\n",
|
|
" self.setto(\"i\")\n",
|
|
" elif self.b[self.k - 1] != 's':\n",
|
|
" self.k = self.k - 1\n",
|
|
" if self.ends(\"eed\"):\n",
|
|
" if self.m() > 0:\n",
|
|
" self.k = self.k - 1\n",
|
|
" elif (self.ends(\"ed\") or self.ends(\"ing\")) and self.vowelinstem():\n",
|
|
" self.k = self.j\n",
|
|
" if self.ends(\"at\"):\n",
|
|
" self.setto(\"ate\")\n",
|
|
" elif self.ends(\"bl\"):\n",
|
|
" self.setto(\"ble\")\n",
|
|
" elif self.ends(\"iz\"):\n",
|
|
" self.setto(\"ize\")\n",
|
|
" elif self.doublec(self.k):\n",
|
|
" self.k = self.k - 1\n",
|
|
" ch = self.b[self.k]\n",
|
|
" if ch in 'lsz':\n",
|
|
" self.k += 1\n",
|
|
" elif self.m() == 1 and self.cvc(self.k):\n",
|
|
" self.setto(\"e\")\n",
|
|
"\n",
|
|
" def step1c(self):\n",
|
|
" \"\"\"step1c() turns terminal y to i when there is another vowel in the stem.\"\"\"\n",
|
|
" if self.ends(\"y\") and self.vowelinstem():\n",
|
|
" self.b = self.b[:self.k] + 'i' + self.b[self.k+1:]\n",
|
|
"\n",
|
|
" def step2(self):\n",
|
|
" \"\"\"step2() maps double suffices to single ones.\n",
|
|
" so -ization ( = -ize plus -ation) maps to -ize etc. note that the\n",
|
|
" string before the suffix must give m() > 0.\n",
|
|
" \"\"\"\n",
|
|
" if self.b[self.k - 1] == 'a':\n",
|
|
" if self.ends(\"ational\"): self.r(\"ate\")\n",
|
|
" elif self.ends(\"tional\"): self.r(\"tion\")\n",
|
|
" elif self.b[self.k - 1] == 'c':\n",
|
|
" if self.ends(\"enci\"): self.r(\"ence\")\n",
|
|
" elif self.ends(\"anci\"): self.r(\"ance\")\n",
|
|
" elif self.b[self.k - 1] == 'e':\n",
|
|
" if self.ends(\"izer\"): self.r(\"ize\")\n",
|
|
" elif self.b[self.k - 1] == 'l':\n",
|
|
" if self.ends(\"bli\"): self.r(\"ble\") # --DEPARTURE--\n",
|
|
" # To match the published algorithm, replace this phrase with\n",
|
|
" # if self.ends(\"abli\"): self.r(\"able\")\n",
|
|
" elif self.ends(\"alli\"): self.r(\"al\")\n",
|
|
" elif self.ends(\"entli\"): self.r(\"ent\")\n",
|
|
" elif self.ends(\"eli\"): self.r(\"e\")\n",
|
|
" elif self.ends(\"ousli\"): self.r(\"ous\")\n",
|
|
" elif self.b[self.k - 1] == 'o':\n",
|
|
" if self.ends(\"ization\"): self.r(\"ize\")\n",
|
|
" elif self.ends(\"ation\"): self.r(\"ate\")\n",
|
|
" elif self.ends(\"ator\"): self.r(\"ate\")\n",
|
|
" elif self.b[self.k - 1] == 's':\n",
|
|
" if self.ends(\"alism\"): self.r(\"al\")\n",
|
|
" elif self.ends(\"iveness\"): self.r(\"ive\")\n",
|
|
" elif self.ends(\"fulness\"): self.r(\"ful\")\n",
|
|
" elif self.ends(\"ousness\"): self.r(\"ous\")\n",
|
|
" elif self.b[self.k - 1] == 't':\n",
|
|
" if self.ends(\"aliti\"): self.r(\"al\")\n",
|
|
" elif self.ends(\"iviti\"): self.r(\"ive\")\n",
|
|
" elif self.ends(\"biliti\"): self.r(\"ble\")\n",
|
|
" elif self.b[self.k - 1] == 'g': # --DEPARTURE--\n",
|
|
" if self.ends(\"logi\"): self.r(\"log\")\n",
|
|
" # To match the published algorithm, delete this phrase\n",
|
|
"\n",
|
|
" def step3(self):\n",
|
|
" \"\"\"step3() dels with -ic-, -full, -ness etc. similar strategy to step2.\"\"\"\n",
|
|
" if self.b[self.k] == 'e':\n",
|
|
" if self.ends(\"icate\"): self.r(\"ic\")\n",
|
|
" elif self.ends(\"ative\"): self.r(\"\")\n",
|
|
" elif self.ends(\"alize\"): self.r(\"al\")\n",
|
|
" elif self.b[self.k] == 'i':\n",
|
|
" if self.ends(\"iciti\"): self.r(\"ic\")\n",
|
|
" elif self.b[self.k] == 'l':\n",
|
|
" if self.ends(\"ical\"): self.r(\"ic\")\n",
|
|
" elif self.ends(\"ful\"): self.r(\"\")\n",
|
|
" elif self.b[self.k] == 's':\n",
|
|
" if self.ends(\"ness\"): self.r(\"\")\n",
|
|
"\n",
|
|
" def step4(self):\n",
|
|
" \"\"\"step4() takes off -ant, -ence etc., in context <c>vcvc<v>.\"\"\"\n",
|
|
" if self.b[self.k - 1] == 'a':\n",
|
|
" if self.ends(\"al\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'c':\n",
|
|
" if self.ends(\"ance\"): pass\n",
|
|
" elif self.ends(\"ence\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'e':\n",
|
|
" if self.ends(\"er\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'i':\n",
|
|
" if self.ends(\"ic\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'l':\n",
|
|
" if self.ends(\"able\"): pass\n",
|
|
" elif self.ends(\"ible\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'n':\n",
|
|
" if self.ends(\"ant\"): pass\n",
|
|
" elif self.ends(\"ement\"): pass\n",
|
|
" elif self.ends(\"ment\"): pass\n",
|
|
" elif self.ends(\"ent\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'o':\n",
|
|
" if self.ends(\"ion\") and (self.b[self.j] == 's' or self.b[self.j] == 't'): pass\n",
|
|
" elif self.ends(\"ou\"): pass\n",
|
|
" # takes care of -ous\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 's':\n",
|
|
" if self.ends(\"ism\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 't':\n",
|
|
" if self.ends(\"ate\"): pass\n",
|
|
" elif self.ends(\"iti\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'u':\n",
|
|
" if self.ends(\"ous\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'v':\n",
|
|
" if self.ends(\"ive\"): pass\n",
|
|
" else: return\n",
|
|
" elif self.b[self.k - 1] == 'z':\n",
|
|
" if self.ends(\"ize\"): pass\n",
|
|
" else: return\n",
|
|
" else:\n",
|
|
" return\n",
|
|
" if self.m() > 1:\n",
|
|
" self.k = self.j\n",
|
|
"\n",
|
|
" def step5(self):\n",
|
|
" \"\"\"step5() removes a final -e if m() > 1, and changes -ll to -l if\n",
|
|
" m() > 1.\n",
|
|
" \"\"\"\n",
|
|
" self.j = self.k\n",
|
|
" if self.b[self.k] == 'e':\n",
|
|
" a = self.m()\n",
|
|
" if a > 1 or (a == 1 and not self.cvc(self.k-1)):\n",
|
|
" self.k = self.k - 1\n",
|
|
" if self.b[self.k] == 'l' and self.doublec(self.k) and self.m() > 1:\n",
|
|
" self.k = self.k -1\n",
|
|
"\n",
|
|
" def stem(self, p, i=0, j=None):\n",
|
|
" \"\"\"In stem(p,i,j), p is a char pointer, and the string to be stemmed\n",
|
|
" is from p[i] to p[j] inclusive. Typically i is zero and j is the\n",
|
|
" offset to the last character of a string, (p[j+1] == '\\0'). The\n",
|
|
" stemmer adjusts the characters p[i] ... p[j] and returns the new\n",
|
|
" end-point of the string, k. Stemming never increases word length, so\n",
|
|
" i <= k <= j. To turn the stemmer into a module, declare 'stem' as\n",
|
|
" extern, and delete the remainder of this file.\n",
|
|
" \"\"\"\n",
|
|
" # copy the parameters into statics\n",
|
|
" self.b = p\n",
|
|
" self.k = j or len(p) - 1\n",
|
|
" self.k0 = i\n",
|
|
" if self.k <= self.k0 + 1:\n",
|
|
" return self.b # --DEPARTURE--\n",
|
|
"\n",
|
|
" # With this line, strings of length 1 or 2 don't go through the\n",
|
|
" # stemming process, although no mention is made of this in the\n",
|
|
" # published algorithm. Remove the line to match the published\n",
|
|
" # algorithm.\n",
|
|
"\n",
|
|
" self.step1ab()\n",
|
|
" self.step1c()\n",
|
|
" self.step2()\n",
|
|
" self.step3()\n",
|
|
" self.step4()\n",
|
|
" self.step5()\n",
|
|
" return self.b[self.k0:self.k+1]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 63,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def processEmail(email_contents, verbose=True):\n",
|
|
" \"\"\"\n",
|
|
" Preprocesses the body of an email and returns a list of indices \n",
|
|
" of the words contained in the email. \n",
|
|
" \n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" email_contents : str\n",
|
|
" A string containing one email. \n",
|
|
" \n",
|
|
" verbose : bool\n",
|
|
" If True, print the resulting email after processing.\n",
|
|
" \n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" word_indices : list\n",
|
|
" A list of integers containing the index of each word in the \n",
|
|
" email which is also present in the vocabulary.\n",
|
|
" \"\"\"\n",
|
|
" # Load Vocabulary\n",
|
|
" vocabList = getVocabList()\n",
|
|
"\n",
|
|
" # Init return value\n",
|
|
" word_indices = []\n",
|
|
"\n",
|
|
" # ========================== Preprocess Email ===========================\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",
|
|
" # hdrstart = email_contents.find(chr(10) + chr(10))\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 starts with < and ends with > and replace\n",
|
|
" # and does not have any < or > in the tag it with a space\n",
|
|
" email_contents =re.compile('<[^<>]+>').sub(' ', email_contents)\n",
|
|
"\n",
|
|
" # Handle Numbers\n",
|
|
" # Look for one or more characters between 0-9\n",
|
|
" email_contents = re.compile('[0-9]+').sub(' number ', email_contents)\n",
|
|
"\n",
|
|
" # Handle URLS\n",
|
|
" # Look for strings starting with http:// or https://\n",
|
|
" email_contents = re.compile('(http|https)://[^\\s]*').sub(' httpaddr ', email_contents)\n",
|
|
"\n",
|
|
" # Handle Email Addresses\n",
|
|
" # Look for strings with @ in the middle\n",
|
|
" email_contents = re.compile('[^\\s]+@[^\\s]+').sub(' emailaddr ', email_contents)\n",
|
|
" \n",
|
|
" # Handle $ sign\n",
|
|
" email_contents = re.compile('[$]+').sub(' dollar ', email_contents)\n",
|
|
" \n",
|
|
" # get rid of any punctuation\n",
|
|
" email_contents = re.split('[ @$/#.-:&*+=\\[\\]?!(){},''\">_<;%\\n\\r]', email_contents)\n",
|
|
"\n",
|
|
" # remove any empty word string\n",
|
|
" email_contents = [word for word in email_contents if len(word) > 0]\n",
|
|
" \n",
|
|
" # Stem the email contents word by word\n",
|
|
" stemmer = PorterStemmer()\n",
|
|
" processed_email = []\n",
|
|
" for word in email_contents:\n",
|
|
" # Remove any remaining non alphanumeric characters in word\n",
|
|
" word = re.compile('[^a-zA-Z0-9]').sub('', word).strip()\n",
|
|
" word = stemmer.stem(word)\n",
|
|
" processed_email.append(word)\n",
|
|
"\n",
|
|
" if len(word) < 1:\n",
|
|
" continue\n",
|
|
"\n",
|
|
" # Look up the word in the dictionary and add to word_indices if found\n",
|
|
" # ====================== YOUR CODE HERE ======================\n",
|
|
"\n",
|
|
" for i in range(len(vocabList)):\n",
|
|
" if word == vocabList[i]:\n",
|
|
" word_indices.append(i)\n",
|
|
"\n",
|
|
" # =============================================================\n",
|
|
"\n",
|
|
" if verbose:\n",
|
|
" print('----------------')\n",
|
|
" print('Processed email:')\n",
|
|
" print('----------------')\n",
|
|
" print(' '.join(processed_email))\n",
|
|
" return word_indices"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 64,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"----------------\n",
|
|
"Processed email:\n",
|
|
"----------------\n",
|
|
"anyon know how much it cost to host a web portal well it depend on how mani visitor your expect thi can be anywher from less than number buck a month to a coupl of dollar number you should checkout httpaddr or perhap amazon ec number if your run someth big to unsubscrib yourself from thi mail list send an email to emailaddr\n",
|
|
"-------------\n",
|
|
"Word Indices:\n",
|
|
"-------------\n",
|
|
"[85, 915, 793, 1076, 882, 369, 1698, 789, 1821, 1830, 882, 430, 1170, 793, 1001, 1894, 591, 1675, 237, 161, 88, 687, 944, 1662, 1119, 1061, 1698, 374, 1161, 476, 1119, 1892, 1509, 798, 1181, 1236, 511, 1119, 809, 1894, 1439, 1546, 180, 1698, 1757, 1895, 687, 1675, 991, 960, 1476, 70, 529, 1698, 530]\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# To use an SVM to classify emails into Spam v.s. Non-Spam, you first need\n",
|
|
"# to convert each email into a vector of features.\n",
|
|
"\n",
|
|
"# Extract Features\n",
|
|
"with open(os.path.join('Data', 'emailSample1.txt')) as fid:\n",
|
|
" file_contents = fid.read()\n",
|
|
"\n",
|
|
"word_indices = processEmail(file_contents)\n",
|
|
"\n",
|
|
"#Print Stats\n",
|
|
"print('-------------')\n",
|
|
"print('Word Indices:')\n",
|
|
"print('-------------')\n",
|
|
"print(word_indices)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h4>2.2 Extracting Features from Emails</h4>\n",
|
|
"We will now implement the feature extraction which converts each email into an n-dimensional vector. We will use n = # words in vocab list. Specificall the i-th feature in {0,1} for an email corresponds to whether the i-th word in the dictionary occurs in the email. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 65,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def emailFeatures(word_indices):\n",
|
|
" \"\"\"\n",
|
|
" Takes in a word_indices vector and produces a feature vector from the word indices. \n",
|
|
" \n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" word_indices : list\n",
|
|
" A list of word indices from the vocabulary list.\n",
|
|
" \n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" x : list \n",
|
|
" The computed feature vector.\n",
|
|
" \"\"\"\n",
|
|
" # Total number of words in the dictionary\n",
|
|
" n = 1899\n",
|
|
" \n",
|
|
" x = np.zeros(n)\n",
|
|
"\n",
|
|
" for i in range(n):\n",
|
|
" if np.any(word_indices == i):\n",
|
|
" x[i] = 1\n",
|
|
" \n",
|
|
" return x"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 66,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"----------------\n",
|
|
"Processed email:\n",
|
|
"----------------\n",
|
|
"anyon know how much it cost to host a web portal well it depend on how mani visitor your expect thi can be anywher from less than number buck a month to a coupl of dollar number you should checkout httpaddr or perhap amazon ec number if your run someth big to unsubscrib yourself from thi mail list send an email to emailaddr\n",
|
|
"\n",
|
|
"Length of feature vector: 1899\n",
|
|
"Number of non-zero entries: 0\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Extract Features\n",
|
|
"with open(os.path.join('Data', 'emailSample1.txt')) as fid:\n",
|
|
" file_contents = fid.read()\n",
|
|
"\n",
|
|
"word_indices = processEmail(file_contents)\n",
|
|
"features = emailFeatures(word_indices)\n",
|
|
"\n",
|
|
"# Print Stats\n",
|
|
"print('\\nLength of feature vector: %d' % len(features))\n",
|
|
"print('Number of non-zero entries: %d' % sum(features > 0))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h4>2.3 Training SVM for Spam Classification</h4>\n",
|
|
"Now that we have functions setup to extract features, we will load a preprocessed training dataset that will be used to train an SVM classifier. spamTrain.mat contains 4000 training samples of spam and non-spam email, while spamTest.mat contains 1000 test samples. Each original email was processed using the processEmail and emailFeatures functions then converted into a 1,899-dimensional vector. After loading the dataset, we will train an SVM to classify between spam and non-spam and test its accuracy."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 74,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Training Linear SVM (Spam Classification)\n",
|
|
"This may take 1 to 2 minutes ...\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load the Spam Email dataset\n",
|
|
"# You will have X, y in your environment\n",
|
|
"data = loadmat(os.path.join('Data', 'spamTrain.mat'))\n",
|
|
"X, y= data['X'].astype(float), data['y'][:, 0]\n",
|
|
"\n",
|
|
"print('Training Linear SVM (Spam Classification)')\n",
|
|
"print('This may take 1 to 2 minutes ...\\n')\n",
|
|
"\n",
|
|
"C = 0.1\n",
|
|
"model = svmTrain(X, y, C, linearKernel)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 75,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Training Accuracy: 99.83\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Compute the training accuracy\n",
|
|
"p = svmPredict(model, X)\n",
|
|
"\n",
|
|
"print('Training Accuracy: %.2f' % (np.mean(p == y) * 100))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 76,
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Evaluating the trained Linear SVM on a test set ...\n",
|
|
"Test Accuracy: 98.80\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load the test dataset\n",
|
|
"# You will have Xtest, ytest in your environment\n",
|
|
"data = loadmat(os.path.join('Data', 'spamTest.mat'))\n",
|
|
"Xtest, ytest = data['Xtest'].astype(float), data['ytest'][:, 0]\n",
|
|
"\n",
|
|
"print('Evaluating the trained Linear SVM on a test set ...')\n",
|
|
"p = svmPredict(model, Xtest)\n",
|
|
"\n",
|
|
"print('Test Accuracy: %.2f' % (np.mean(p == ytest) * 100))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<h4>2.4 Top Predictors for Spam</h4>\n",
|
|
"To better understand how the spam classifier works, we can inspect the parameters to see which words the classifier thinks are most productive of spam. We will now find the parameters with the largest positive values in the classifier and display the corresponding words."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 78,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Top predictors of spam:\n",
|
|
"word weight \n",
|
|
"---- ------\n",
|
|
"our 0.50\n",
|
|
"click 0.47\n",
|
|
"remov 0.42\n",
|
|
"guarante 0.39\n",
|
|
"visit 0.37\n",
|
|
"basenumb 0.35\n",
|
|
"dollar 0.32\n",
|
|
"will 0.27\n",
|
|
"price 0.27\n",
|
|
"pleas 0.26\n",
|
|
"most 0.26\n",
|
|
"nbsp 0.25\n",
|
|
"lo 0.25\n",
|
|
"hour 0.24\n",
|
|
"ga 0.24\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Sort the weights and obtin the vocabulary list\n",
|
|
"# NOTE some words have the same weights, \n",
|
|
"# so their order might be different than in the text above\n",
|
|
"idx = np.argsort(model['w'])\n",
|
|
"top_idx = idx[-15:][::-1]\n",
|
|
"vocabList = getVocabList()\n",
|
|
"\n",
|
|
"print('Top predictors of spam:')\n",
|
|
"print('%-15s %-15s' % ('word', 'weight'))\n",
|
|
"print('----' + ' '*12 + '------')\n",
|
|
"for word, w in zip(np.array(vocabList)[top_idx], model['w'][top_idx]):\n",
|
|
" print('%-15s %0.2f' % (word, w))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"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": "3.7.3"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|