{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 11 - Support Vector Machines\n", "\n", "by [Alejandro Correa Bahnsen](albahnsen.com/)\n", "\n", "version 0.2, May 2016\n", "\n", "## Part of the class [Machine Learning for Security Informatics](https://github.com/albahnsen/ML_SecurityInformatics)\n", "\n", "\n", "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 3.0 Unported License](http://creativecommons.org/licenses/by-sa/3.0/deed.en_US). Special thanks goes to [Jake Vanderplas](http://www.vanderplas.com)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previously we introduced supervised machine learning.\n", "There are many supervised learning algorithms available; here we'll go into brief detail one of the most powerful and interesting methods: **Support Vector Machines (SVMs)**." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "plt.style.use('fivethirtyeight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Motivating Support Vector Machines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Support Vector Machines (SVMs) are a powerful supervised learning algorithm used for **classification** or for **regression**. SVMs are a **discriminative** classifier: that is, they draw a boundary between clusters of data.\n", "\n", "Let's show a quick example of support vector classification. First we need to create a dataset:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACm\nQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgB\nAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACm\nQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgB\nAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAACm\nQjgBAACmQjgBAACmQjgBAACmQjgBAACmQjgBAMDJ7DU1Rrfg0ZweTqZPn66LL75YCQkJSkpK0qhR\no7R9+3Zn7wYAANM5tm2b1k2ZogVDh2rd00/r2LZtRrfkkXyc/YZr167V2LFj1b17d9XW1uqpp57S\niBEjtH79eoWHhzt7dwAAmMKxH37Q/KFDVVFQIEk6/PXX2vzqq7r2ww8VnZZmcHeexenhZMGCBfW+\nfuWVV5SQkKD169dr8ODBzt4dAACmsGvJkrpg8ouKggJlLllCOGkil19zUlRUJLvdzlETAIDXqqmu\n1sEvvnC47eAXX3ANShO5PJw89NBDysjIUO/evV29KwBoto7v26eDa9Yoe9MmVRQVGd1Os2Pz8VHb\nCy90uK3thRfKarO5uSPP5tJw8vDDD2vDhg166623ZLFYXLkrAGiW7NXV+vHDDzV3wAAtHDZM8y66\nSB/fcYcK9u0zurVmJ2XkSPmFhdWr+YWHK2nECIM68lyWgoKCWle88eTJk7VkyRJ98MEHSkxM/M3X\nZ2ZmuqINAPBqvnl5Wjp0qOzV1fXqXcaOVeK4caridILbWK1W+eTl6cBHH+nwV1+pTb9+Srj8clVH\nRsputxvdnsslJyc77b1cEk4mTZqk999/Xx988IGSkpKc/fYeJTMz06kTZibePDaJ8Xkybx6bVH98\nO+bP18djxzZ4jc3PT7ds2KCwdu3c3d5Z84b5q6muls2n4T0n3jA2d3D63ToPPPCA/v3vf+udd95R\naGiocnJyJElBQUEKCgpy9u4AoFmrrT3F75enqsMtHAUTNJ7TrzmZM2eOiouLdeWVV6pz5851f15+\n+WVn7woAmr3o1FRZHFxsmX7LLQpu08aAjoCz5/Rol5+f7+y3BACcQmTnzhr6z3/qk/HjVfnzXTpt\nBw5UjwmDB/WMAAAgAElEQVQTZPP1Nbg74Mxw3AkAPJjN11eJw4bphnPOUeGBA2oRHKzwpCT5/+qu\nEcCTEE4AwMNZLBaFd+ig8A4djG4FcAqeSgwAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIA\nAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEyFcAIAAEzFx+gGAMAb\nVZaUqHDfPtmrqxUSH6+AqCijWwI8BuEEAJysYM8erXnsMe1etkySFJWWpstmzFBs9+4GdwZ4Bk7r\nAIATVZWV6asnnqgLJpKUu22b3r/uOhUeOGBgZ4DnIJwAgBMd37dPme+/36BeevSo8nbtMqAjwPMQ\nTgDAiWqrq6XaWofbaior3dwN4JkIJwDgRCFt2yq2Z88GdZufnyKSkgzoCPA8hBMAcCL/8HAN+r//\nU1Dr1nU1m7+/fvfGG4QToJG4WweA6VVXVKhg926VHD2qwOhoRSQny8fPz+i2Tqll164a9dlnytu5\nUzVVVQrv2FERiYmyWPl9EGgMwgkAUyvLzdXmf/xDG6ZPV21NjSxWq3r+4Q/qcc89CoyONrq9UwqJ\ni1NIXJzRbQAeiRgPwNQOr1+v9c89p9qaGklSrd2ub194QYe++srgzgC4CuEEgNvVVFerury8Ua/9\n4V//cljf+sYbqqmudmZbzU5VWZnydu1SXmZmo+cDcAdO6wBwm8qSEv20YYM2v/aaSnNylH7TTWo3\naJBC27Y99Ted6joNq1UWi8U1jTYDeZmZWvvkk9q9bJksFotSrr5afSZPVkTHjka3BhBOALjPng8/\n1Mdjx9Z9/dO336rdJZdo8KxZCoyJcfg9XW65RXuWL29Q7/r738tqs7msV29Wlpur/9x1l7I3bpQk\n1dbWauf8+SrNydGwt96SX1iYwR2iueO0DgC3KDp0SF88/HCD+v7PPlPujh11X5dkZ6vw4EFVV1RI\nklqfd576PvqorL6+kiSrj4/Oe+ghxfXt657GvVD+7t11weRkB1evVsGePQZ0BNTHkRMAblFx/LhK\njx51uK00J0elx45p97JlWv/MMyrLzVXKyJE69777FJ2Wpp5/+IMShw1T6dGjCoyKUnhSkmw/hxU0\n3emuL6kqK3NjJ4BjhBMAbuEfEaHgNm1UfPhwg23BrVtr5/z5Wj15cl1tx7//rayvvtJ1H32k0IQE\nRXXqpKhOndzZstcKa9dOfmFhqjh+vF49sGVLhbVrZ1BXwP9wWgeAWwS3bq2BzzzToJ585ZUKjI3V\n11OnNthWfOiQjv3wgzvaa1bC2rfXkNmzZTtpITufgAANee011maBKXDkBIDbtL/0Ul374YfaNm+e\nSrKzlXrddYrr10+VxcUNfov/RUVhoZu7bB7aDxqkG1avVt6uXbJYLIpMSVFESorRbQGSCCcA3MjH\n319xffs2uJi1/Phxte7dW0c2bGjwPeHc2uoSFqtVUZ07K6pzZ6NbARrgtA4Aw/mHhWnA00+rRUhI\nvXqv++/nhyfQDHHkBIAptDr3XF3/2WfK+e47VeTnK6ZLF0WlpzcILAC8H+EEgGlwR445VVdUqOTI\nEVl8fBQSF8fKvHA5TusAAE4pd+dOfTphgv7Zo4f+1aePNjz3nIoc3A4OOBNHTgAADhUfOaJlN96o\ngt27JUlVxcVa9/TTKj9+XBf89a8shAeX4cgJAMCh3B076oLJyb579VUV7tvn/obQbBBOAAAOVRUX\nO6zbq6pUVVrq5m7QnBBOAAAOhXXoIIu14Y+JiJQUBbOSLFyIcAIAcCgiOVkDn3uuXs0nMFCXvPii\nAqOjDeoKzQEXxAIAHPLx81P6DTcotls35e3cKZu/v6LT07ndGy5HOAEAnJJPQIBa9eypVj17Gt0K\nmhFO6wAAAFPhyAmAempra1WUlSV7dbWCW7WST0CA0S0BaGY4cgKgTtGhQ/p66lT9q08f/bNHD318\n993K3bHD6LYANDMcOQEgSaqpqtLGmTO1acaMutru99/X0S1bdM3y5Qpp08bA7vBrtXa7crZsUdaa\nNSo7dkxtBwxQy4wMBURGGt0acNYIJwAkSYX79um7V19tUD++d6/yduwgnJiIxWLRwS+/1JJrrpG9\nqkqS9O0LL6j7uHHqM3my/EJD672++MgRHd26VQV79ii0bVvFZGQoND7eiNaBRiGcAJAkVZWV1f2g\n+7XKU6wUCmO0qK7WivvvbzBfm2bNUspVV6l1r151tcIDB/TxnXfq8Ndf19Wi0tI07O23FdGxo9t6\nBpqCa04ASJKC27RRZOfODeoWq1Xh/BAzFXtRkcNn3kgnwsjJDn75Zb1gIkm527Zpz/LlLusPOFuE\nEwCSpMDoaF3y4ovyDQqqV7/o+ecVkZxsUFdwxOrvL7+wMIfb/CMi6n29e+lSh6/buWCBqsrKnN4b\n4Ayc1gFQp81552n0ypU6tm2bqsvLFZWSoqjUVPn4+RndGk5SExys8//yF63685/r1aPPOUdRqakq\nPXZMx374QVUlJQpt187he4QlJsrm6+uOdoEmI5wAqCcyJUWRKSlGt4HTqK6uVqdrrlFAVJTWP/+8\nKgoKlHbDDUobPVq1NTX6zz33aP/nn0uSBkyZIquPj+zV1f97A4tFGXfcIasPPwJgTvzNBAAPFBAZ\nqU5XX612gwapprJSgTExslgs+uHtt+uCiSRtfuUV9X/6ae3497+VvXGjotLSdOETT6jVueca2D1w\neoQTAPBg/uHhdf9tr6nRtnnz6m0/vm+fvvjLX9Tz3nt1+Zw58gsNbXBdCmA2Lrkgdu3atRo9erTS\n0tIUERGheb/6xwIAcD6rzaaQuLgGdXtVlQoPHlRoQgLBBB7BJeGkpKRE6enpmjp1qgIDA12xCwCA\nA+eMGeOw3mXMGFksFjd3A5wZl4STSy+9VI888oiGDx/OPwYAcKNWPXvqinfeUUjbtpKkkLZtNezt\nt7nGBB6Fa04AwIv4+PsrcehQtTr3XFUUFMgvPFxBsbFGt3VaNVVVKvjxRx3ft0++QUHyj442uiUY\njHACAF4oKDbW9KFEkqorKpS5eLE+vffeuuX4o9LSNPSf/+SW9mbMUlBQUOvKHcTHx+u5557T6NGj\nT/u6zMxMV7YBADAh32PHtOR3v5Nq6/8oSrnmGqVPnqxKu92gztBUyU5cSdo0R06cOSgzyczMZGwe\nivF5Jnt1tQ5u2SLf6moFxsQorH17U137VpKdrbydO1VZXKyw9u0VkZzc5JVavWnutm/a1CCYSFLm\nokXq+5e/KDwx0YCuXMeb5s6VTBNOAOBsleXmassbb2jDc8+ppqJCvsHB6v/00+p09dVq8atnBhkh\nb9cuLR8zRrnbt0uSrD4+umj6dHW+9lr5BgQY3J0xbKdYpdbm5yerzebmbmAWLruVeOvWrdqyZYvs\ndruysrK0detWZWVluWJ3ACBJOvjFF1r3t7+ppqJCklRVXKzP//AHZW/caHBnJ66t2PD883XBRDpx\nlOfzP/xBeSfVmpuotDTZ/P0b1DPuvFMh8fEGdAQzcEk42bRpk/r376+BAweqvLxcU6ZM0YABAzRl\nyhRX7A4AVFVWpk3/+IfDbbs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_blobs\n", "X, y = make_blobs(n_samples=50, centers=2,\n", " random_state=0, cluster_std=0.60)\n", "plt.figure(figsize=(8,8))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A discriminative classifier attempts to draw a line between the two sets of data. Immediately we see a problem: such a line is ill-posed! For example, we could come up with several possibilities which perfectly discriminate between the classes in this example:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SkxMiPejZ0wM2NhI0NbW2aZ82rR8CA1kcj8gSyGQyzJ07F9evX1frs7W1RVJS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xfit = np.linspace(-1, 3.5)\n", "plt.figure(figsize=(8,8))\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "\n", "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n", " plt.plot(xfit, m * xfit + b, '-k')\n", "\n", "plt.xlim(-1, 3.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are three *very* different separaters which perfectly discriminate between these samples. Depending on which you choose, a new data point will be classified almost entirely differently!\n", "\n", "How can we improve on this?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Support Vector Machines: Maximizing the *Margin*\n", "\n", "Support vector machines are one way to address this.\n", "What support vector machined do is to not only draw a line, but consider a *region* about the line of some given width. Here's an example of what it might look like:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VkpIS9t8RBSeEkG4ZPToD06fno6Kipt3xFStmo6BAmaWw+5rq6jYcOFCLr7++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\nyiUlJQU1NTW9lkAfO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xfit = np.linspace(-1, 3.5)\n", "plt.figure(figsize=(8,8))\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "\n", "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n", " yfit = m * xfit + b\n", " plt.plot(xfit, yfit, '-k')\n", " plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n", "\n", "plt.xlim(-1, 3.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice here that if we want to maximize this width, the middle fit is clearly the best.\n", "This is the intuition of **support vector machines**, which optimize a linear discriminant model in conjunction with a **margin** representing the perpendicular distance between the datasets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Fitting a Support Vector Machine\n", "\n", "Now we'll fit a Support Vector Machine Classifier to these points. While the mathematical details of the likelihood model are interesting, we'll let you read about those elsewhere. Instead, we'll just treat the scikit-learn algorithm as a black box which accomplishes the above task." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n", " decision_function_shape=None, degree=3, gamma='auto', kernel='linear',\n", " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", " tol=0.001, verbose=False)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.svm import SVC # \"Support Vector Classifier\"\n", "clf = SVC(kernel='linear')\n", "clf.fit(X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_svc_decision_function(clf, ax=None):\n", " \"\"\"Plot the decision function for a 2D SVC\"\"\"\n", " if ax is None:\n", " ax = plt.gca()\n", " x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n", " y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n", " Y, X = np.meshgrid(y, x)\n", " P = np.zeros_like(X)\n", " for i, xi in enumerate(x):\n", " for j, yj in enumerate(y):\n", " P[i, j] = clf.decision_function([xi, yj])\n", " # plot the margins\n", " ax.contour(X, Y, P, colors='k',\n", " levels=[-1, 0, 1], alpha=0.5,\n", " linestyles=['--', '-', '--'])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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C2QWVKgpSqUTQHwBUKpVHiPAWILRaLe64445+XiUNVwwcFDG0WgV++csZKC1N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\n11/XZ599pg8//JB9Z5bde++9qq6u1qFDh/TCCy+opKREdXV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "plot_svc_decision_function(clf);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the dashed lines touch a couple of the points: these points are the pivotal pieces of this fit, and are known as the *support vectors* (giving the algorithm its name).\n", "In scikit-learn, these are stored in the ``support_vectors_`` attribute of the classifier:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YFcouqFRRkEolgv4AoFKpPEKEtwCh1Wpxxx139PMqabhi4KCIodUq8KtfzUBp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\nahXgdAISCcqWLcOkBx+EJikp2MOjXjhplIiIwlL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,8))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "plot_svc_decision_function(clf)\n", "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use IPython's ``interact`` functionality to explore how the distribution of points affects the support vectors and the discriminative fit.\n", "(This is only available in IPython 2.0+, and will not work in a static view)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VSo0rV8qwa1cmCgpqMW5cMHr39rLIgKxXLw8kJ98waO/Xzwsikel3jDWVmppG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\nkJ1djTt3amBvz0VoqLTTlfg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2iS4okOHMmUKkpGQjKMgBo0YFISbGFTNmRGH06CA0NWl0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\no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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.html.widgets import interact\n", "\n", "def plot_svm(N=10):\n", " X, y = make_blobs(n_samples=200, centers=2,\n", " random_state=0, cluster_std=0.60)\n", " X = X[:N]\n", " y = y[:N]\n", " clf = SVC(kernel='linear')\n", " clf.fit(X, y)\n", " plt.figure(figsize=(8,8))\n", " plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", " plt.xlim(-1, 4)\n", " plt.ylim(-1, 6)\n", " plot_svc_decision_function(clf, plt.gca())\n", " plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none')\n", " \n", "interact(plot_svm, N=[10, 200], kernel='linear');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the unique thing about SVM is that only the support vectors matter: that is, if you moved any of the other points without letting them cross the decision boundaries, they would have no effect on the classification results!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Going further: Kernel Methods\n", "\n", "Where SVM gets incredibly exciting is when it is used in conjunction with *kernels*.\n", "To motivate the need for kernels, let's look at some data which is not linearly separable:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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zyzBiRBc8+GAiEhN9rF0a2TCJvT16PvYYru7fb3Asdto0AIDYzg7dH3kEF7/5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\nZAeLrw0YENzK1aA1EWgAwMkdO1aklJS/Kzr6Dd1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KKpSXV2qHigAALUGggVPz9XVv0WsA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\nYHj/H07LocfhMc4EAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_circles\n", "X, y = make_circles(100, factor=.1, noise=.1)\n", "\n", "clf = SVC(kernel='linear').fit(X, y)\n", "plt.figure(figsize=(8,8))\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "# plot_svc_decision_function(clf);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, no linear discrimination will ever separate these data.\n", "One way we can adjust this is to apply a **kernel**, which is some functional transformation of the input data.\n", "\n", "For example, one simple model we could use is a **radial basis function**" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot this along with our data, we can see the effect of it:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HbrcbjhwDR2OxGCKRSLJYVzAYRCQSKapbgQIIE5jeMtCTQzEUPQbIaU223bER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\n+onWyZNP3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Y9I2iPGSotMhMDFixcxceJErFu3ThYCMg6FLAZkJA2XTGx+fn6U+ysUClbZ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\nIivHMEBERGTlGAaIiIis3H9dbVOTsG5yRgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits import mplot3d\n", "\n", "def plot_3D(elev=30, azim=30):\n", " plt.figure(figsize=(8,8))\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50)\n", " ax.view_init(elev=elev, azim=azim)\n", " ax.set_xlabel('x')\n", " ax.set_ylabel('y')\n", " ax.set_zlabel('r')\n", "\n", "interact(plot_3D, elev=[-90, 90], azip=(-180, 180));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that with this additional dimension, the data becomes trivially linearly separable!\n", "This is a relatively simple kernel; SVM has a more sophisticated version of this kernel built-in to the process. This is accomplished by using ``kernel='rbf'``, short for *radial basis function*:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QGBgIsVgMHx8fcDgck9VmzTgcDjZv3sx0GcTKUEgh00Yq7cfbbxsubKbVAtnZ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\n1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = SVC(kernel='rbf')\n", "clf.fit(X, y)\n", "\n", "plt.figure(figsize=(8,8))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50)\n", "plot_svc_decision_function(clf)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here there are effectively $N$ basis functions: one centered at each point! Through a clever mathematical trick, this computation proceeds very efficiently using the \"Kernel Trick\", without actually constructing the matrix of kernel evaluations.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }