{ "metadata": { "name": "07A_in_depth_with_SVMs" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "import numpy as np\n", "import pylab as pl" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 0 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "In depth with SVMs: Support Vector Machines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "SVM stands for \"support vector machines\". They are efficient and easy to use estimators.\n", "They come in two kinds: SVCs, Support Vector Classifiers, for classification problems, and SVRs, Support Vector Regressors, for regression problems." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import svm" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python2.7/site-packages/scikits/__init__.py:1: UserWarning: Module argparse was already imported from /usr/local/Cellar/python/2.7.5/Frameworks/Python.framework/Versions/2.7/lib/python2.7/argparse.pyc, but /usr/local/lib/python2.7/site-packages is being added to sys.path\n", " __import__('pkg_resources').declare_namespace(__name__)\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Linear SVMs: some intuitions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To develop our intuitions, let us look at a very simple classification problem: classifying irises based on sepal length and width. We only use 2 features to enable easy visualization." ] }, { "cell_type": "code", "collapsed": false, "input": [ "svc = svm.SVC(kernel='linear')\n", "from sklearn import datasets\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2]\n", "y = iris.target\n", "svc.fit(X, y)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 4, "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, shrinking=True,\n", " tol=0.001, verbose=False)" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize the prediction, we evaluate it on a grid of points:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from matplotlib.colors import ListedColormap\n", "# Create color maps for 3-class classification problem, as with iris\n", "cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])\n", "cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])\n", "\n", "def plot_estimator(estimator, X, y):\n", " estimator.fit(X, y)\n", " x_min, x_max = X[:, 0].min() - .1, X[:, 0].max() + .1\n", " y_min, y_max = X[:, 1].min() - .1, X[:, 1].max() + .1\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, 100),\n", " np.linspace(y_min, y_max, 100))\n", " Z = estimator.predict(np.c_[xx.ravel(), yy.ravel()])\n", "\n", " # Put the result into a color plot\n", " Z = Z.reshape(xx.shape)\n", " pl.figure()\n", " pl.pcolormesh(xx, yy, Z, cmap=cmap_light)\n", "\n", " # Plot also the training points\n", " pl.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)\n", " pl.axis('tight')\n", " pl.axis('off')\n", " pl.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_estimator(svc, X, y)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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nvs/+/asxmYLo02c8DRq4VtllJ56+B5XtKijhGzJTBfXEyJsiMhmZqCuyDPn8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\n1xmPHU9kD5MmdePixXo4HJHcvj2HqVN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} ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, `kernel=\"linear\"` gives linear decision frontiers: the frontier between two classes is a line.\n", "\n", "How does multi-class work? With the `SVC` object, it is done by combining \"one versus one\" decisions on each pair of classes.\n", "\n", "**LinearSVC**: for linear kernels, there is another object, the `LinearSVC` that uses a different algorithm. On some data it may be faster (for instance sparse data, as in text mining). It uses a \"one versus all\" strategy for multi-class problems." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot_estimator(svm.LinearSVC(), X, y)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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Tyf6k2zuAG4risWHrhYKDceh0rEu6fQw46HTyRJEiHjmeL1pO13/+E0JIBZXp/PjBB0zQ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\n4FqDiWwTibOlE8McP8persP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} ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "SVRs (Support Vector Regression) work like SVCs, but for regression rather than classification." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Support vectors and regularisation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Support vectors**: The way a support vector machine works is by finding a decision boundary separating the 2 classes that is spanned by a small number of training samples, called \"support vectors\". These samples lie closest to the other class, and can thus be considered as most representative samples in terms of the two-class discrimination problem.\n", "\n", "To make visualization even simpler, let us consider a 2 class problem, for instance using classes 1 and 2 in the iris dataset. These 2 classes are not well linearly separable, which makes it an interesting problem.\n", "\n", "The indices of the support vectors for each class can be found in the `support_vectors_` attribute. We highlight them in the following figure." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X, y = X[np.in1d(y, [1, 2])], y[np.in1d(y, [1, 2])]\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "output_type": "display_data", "png": 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YIpFISUiIYOvWseh0WiZMOIBUavBeYofn3x+tVvOX40b+jkaj/tuy/v7H8Pbuz+DBa6lZ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\nyF3iE6Ko68nDVxLkjEoUVZKghMgHi8XCyZgYom/fpqSzM81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} ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Regularization**: Considering only the discriminant samples is a form of regularization. Indeed, it forces the model to be simpler in how it combines observed structures.\n", "\n", "This regularization can be tuned with the *C* parameter:\n", "\n", "- Low C values: many support vectors... Decision frontier = mean(class A) - mean(class B)\n", "- High C values: small number of support vectors: Decision frontier fully driven by most disriminant samples" ] }, { "cell_type": "code", "collapsed": false, "input": [ "svc = svm.SVC(kernel='linear', C=1e3)\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)\n", "pl.title('High C values: small number of support vectors')\n", "\n", "svc = svm.SVC(kernel='linear', C=1e-3)\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)\n", "pl.title('Low C values: high number of support vectors')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "output_type": "display_data", "png": 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bpnHr1kmmTTtVyFFKUk5yJQnpP+t1T9wNDt7PsmV99SfpqtVKDA2Nad58MJ9+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\no5Htp09z/No1fhk5Mt+0DjIajdQeN47LERG87eVFg0qV+PPBA3acPYv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Kekj37nOYNu0kly/vZvfuGcUdpiQVIBOUJBVSRk4OfoGB7Bozhm+2/8zwtb9w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} ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One nice features of SVMs is that on many datasets, the default value 'C=1' works well.\n", "\n", "**Practical note: Normalizing data** For many estimators, including the SVMs, having datasets with unit standard deviation for each feature is often important to get good prediction." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Kernels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One appealling aspect of SVMs is that they can easily be used to build non linear decision frontiers using **kernels**. Kernel define the 'building blocks' that are assembled to form a decision rule.\n", "\n", "- **linear** will give linear decision frontiers. It is the most computationally efficient approach and the one that requires the least amount of data.\n", "\n", "- **poly** will give decision frontiers that are polynomial. The order of this polynomial is given by the 'order' argument.\n", "\n", "- **rbf** uses 'radial basis functions' centered at each support vector to assemble a decision frontier. The size of the RBFs, that ultimately controls the smmothness of the decision frontier. RBFs are the most flexible approach, but also the one that will require the largest amount of data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "svc = svm.SVC(kernel='linear')\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)\n", "pl.title('Linear kernel')\n", "\n", "svc = svm.SVC(kernel='poly', degree=4)\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)\n", "pl.title('Polynomial kernel')\n", "\n", "svc = svm.SVC(kernel='rbf', gamma=1e2)\n", "plot_estimator(svc, X, y)\n", "pl.scatter(svc.support_vectors_[:, 0], svc.support_vectors_[:, 1], s=80, facecolors='none', zorder=10)\n", "pl.title('RBF kernel')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "output_type": "display_data", "png": 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D/v0X07x5daysvsPObgWTJnliZGSKj8923N2H5mkcnTpNIi4ujMqVG9OwYSf0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\nS6NW46hWE53/2ARcUijw/JuYPV1cuHu+ZAEiHRzwLFWq4PW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SJCZMqImb27e4u3dn+vQmPEtOxs6+NFOm+LByZV/09Q0YOHBtHt2ZkJ/EXnyC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\nWamEhu7N6yRRteqLRWZpufh3ElAPk4AqkIxGIyc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LlnTE1XUiuroG6Ooa4OIylDVrBvLNN4epXqcNVlG7GGRtTVM7O/r//DNdGzWi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} ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that RBFs and more flexible and fit our train data best. Remember, minimizing train error is not a goal per se, and we have to watch for overfit." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Exercise: tune an SVM on the digits dataset" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import datasets\n", "digits = datasets.load_digits()\n", "X, y = digits.data, digits.target\n", "#... now all that is left to do is the prediction" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 } ], "metadata": {} } ] }