{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 12 - 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 Risk Management](https://github.com/albahnsen/ML_RiskManagement)\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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\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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/fckrNiNHjsQzzzyDyZMndzou1o+IK2z8WbCrUqmg1+uhVvs/OjCcEFGfDRsW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\n8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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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HSmjbtm1DXV2dqN1ut4sCCNC3rsPpdAamUgRBQF5eXtCUSiyNGjKAUNLIy1Oj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\n9mw82G6pGpGvKj9zBj+tXYsL//0vYvv1Q99586DIzYVIzCehriKLj4c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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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JXH5jou8fH7YeL78MZWwsAECuVMI/JcXs+Z6tWhl97dumDdxDQkxe1+Pll+HO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\nOzoeAABwQw4vNOvWrdOiRYtksVhksViUkpIiSVq5cqUmT54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"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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EAiQGDERaQIgVtFgDnLQjFqOnCGLtvpeKVByUEtktFQfSqG4njjXCPKTiIJVKFYyhccr4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\ns2oVrx8r17YYU3y5KYzFuq9YdxNIEc9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j+uuvx6ZNm9Da2ir7mW9+85t49dVX8Q//8A9Y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\nELhw4QLGjBmDNm3aw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"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": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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aHgoPD3/kGKqrO7FmzT5Ipffn0xQXt+Lf/u0Etm9fCg+P0f2ZCbEUtLqHEBulUCigVBqX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\n0vz587udk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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 }