{ "metadata": { "name": "", "signature": "sha256:091cd16ff2d7ebd980c0128c65dfa4077438a75132eff854696d2dacbf51f171" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Supervised Learning In-Depth: Support Vector Machines" ] }, { "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", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "\n", "# use seaborn plotting defaults\n", "import seaborn as sns; sns.set()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "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", "collapsed": false, "input": [ "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.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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XFBHxQfn5dcrclpdX14tJAteAAT8hLW0qs2fPAqBTp8m0bx9tcSrf4MmR8c+B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\n3ozvsZ49v89HHy3nsce+LF4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"text": [ "" ] } ], "prompt_number": 2 }, { "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", "collapsed": false, "input": [ "xfit = np.linspace(-1, 3.5)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\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);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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iIeEkSUkJnD17msOHDzX7OSQZi3bj7OzMhEWT1Q5DCIvg7OzM3L8vIj8vH92V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\nvHkL3nprPjNmzKRxY/tfClAI8WS6dOlLly4y21w8TIqxDRQ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"text": [ "" ] } ], "prompt_number": 3 }, { "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*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "collapsed": false, "input": [ "xfit = np.linspace(-1, 3.5)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\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);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sCNK8Xp7n8ODBA1RV7cPRo0dht9ug1erw4osvobx8OwoLp8PlYodtHMGQ5gcb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\nbkxxJBKJ1ARlaf7g+lav5u+1WKytcjJx6dJXbNiwhs2bN+P3+3E6neT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"text": [ "" ] } ], "prompt_number": 4 }, { "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", "collapsed": false, "input": [ "from sklearn.svm import SVC # \"Support Vector Classifier\"\n", "clf = SVC(kernel='linear')\n", "clf.fit(X, y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.0,\n", " kernel='linear', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False)" ] } ], "prompt_number": 5 }, { "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", "collapsed": false, "input": [ "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", " return ax.contour(X, Y, P, colors='k',\n", " levels=[-1, 0, 1], alpha=0.5,\n", " linestyles=['--', '-', '--'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YZKUpSrFoNBpMmjRF1k7UkjDhEoWI6tIUi8WimLS2bNmIsrIy38Lw1Qn0W9/6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\nVbKVJODePQ1u376K8vI1ePH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"text": [ "" ] } ], "prompt_number": 7 }, { "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", "collapsed": false, "input": [ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf)\n", "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Nt9uluVKQ0+nkL3/5o6rdYDBoJlyz2UzXrt2wWCz+khSTyYTFop30TCYTL7zw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\n7FFnKaFo26SHK0SEOXp0GzdvbsDr1ZO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"text": [ "" ] } ], "prompt_number": 8 }, { "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", "collapsed": false, "input": [ "from IPython.html.widgets import interact\n", "\n", "def plot_svm(N):\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.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\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');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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G2hn9w/Ek6bRB2X5n1+2Z7pzee5r8qny/5euGfcSsJU8EfXszfzGPFbEfkLgtjtSyVG5m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\nODhUUVbWlwED3qJjRyu1FZvQ5MnvceJEAikp3+DoqMNkGsCkSYvRas2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"text": [ "" ] } ], "prompt_number": 9 }, { "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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "collapsed": false, "input": [ "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", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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E1q5V8gaqMbUmZnVFI8qk/38PZnafuRgx5rcl+iay/9nDPNGzvQcjcx+1/uGo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\n8c47y/jmN6/nvPNGeB1OTKSmpjLl3mleh9FjqqqqSH85uTE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"text": [ "" ] } ], "prompt_number": 10 }, { "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", "collapsed": false, "input": [ "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot this along with our data, we can see the effect of it:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits import mplot3d\n", "\n", "def plot_3D(elev=30, azim=30):\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='spring')\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));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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FRKxd+wnceON9RRd6q3QXAAkCmmnxheTpLpSfoAJDk3sYoG88TlH2ghkMTmP//n0mwXSW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"text": [ "" ] } ], "prompt_number": 12 }, { "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", "collapsed": false, "input": [ "clf = SVC(kernel='rbf')\n", "clf.fit(X, y)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n", "plot_svc_decision_function(clf)\n", "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n", " s=200, facecolors='none');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sLBx//4B7Vb9+Zl9qsra2JigomKCggfG2XV2dNDQ0UF+vD9QNDfVcu1bMtWvF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"text": [ "" ] } ], "prompt_number": 13 }, { "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", "\n", "We'll come back to SVMs in the breakout session following this lecture." ] } ], "metadata": {} } ] }