{ "metadata": { "name": "", "signature": "sha256:a33fe472e88f009984bbf961d05c6cbb5494ca70a0b50c0ecba05b401b914a87" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com) for PyData Seattle 2015. Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_pydata2015/)." ] }, { "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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C0sPIbJZFnUej6TRGr2+L/1AZB7hlv1/EA2/2pb6jfvHYynUrOfKWg+aJhoXJqpaje46Q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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*\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", "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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mi1uwgCAiAcPYoNfrYTKFPh7McZzXalb8cRlcuvQZKisPoqGhHgAwe/ZsVFS8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\n79ecODGdpKSBT/w7nnQtevYcRc+ewV7SkXLNfL66a9IhOEIuLX0QMXE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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", " # plot the margins\n", " 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=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.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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kJBoaGsnMzNww7t26kYWIN5ZlMTo6gmmeR2vNwsI8ABkZmRw+3IFSBtXVNRK4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\n73O5TuFynWJycpKkJAcuV+G+We5uYOA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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\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", "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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Msibt+Tb57PvPdCa+2fxlHjtCf5iT9MdD1tYXNTU1rFu3llu3bhIePoQpU6Lb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\nRU5ErkJggg==\n", "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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Yx+rVayCKIiYnJxGJhOH11qGjo4PS85idXNqkkWR44mFRFNni+6Vs2s0szHRUioAXS00I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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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K1ej1ei5dqmT37h2sXr1OpPIchR7269ZaQKlWq2eqVKrpwKu3jt02CXhOrVYX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\nXy/j+PGTfP75p6xfvxGpdPZUN01gEmhoqOfMmVN0dXVhZ2fH6tVrp0Q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44/AeLr93zuBJ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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 leave SVMs for the time being and take a look at another classification algorithm: Random Forests." ] } ], "metadata": {} } ] }