{ "metadata": { "name": "04A_supervised_classification" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Supervised Learning: Classification of Handwritten Digits" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section we'll apply scikit-learn to the classification of handwritten\n", "digits. This will go a bit beyond the iris classification we saw before: we'll\n", "discuss some of the metrics which can be used in evaluating the effectiveness\n", "of a classification model.\n", "\n", "We'll work with the handwritten digits dataset which we saw in an earlier\n", "section of the tutorial." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 0 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll re-use some of our code from before to visualize the data and remind us what\n", "we're looking at:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "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": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# copied from notebook 02A_representation_of_data.ipynb\n", "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", "\n", "# plot the digits: each image is 8x8 pixels\n", "for i in range(64):\n", " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", " ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n", " \n", " # label the image with the target value\n", " ax.text(0, 7, str(digits.target[i]))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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WNDU1IRgMYsmSJXj99dexbNmyG/6dmfi1osdOS01Nxdq1azFv3jwMGTIE4XAY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\nwoGPiIh8hQMfERH5Cgc+IiLylf8HYwGtAoXEvwsAAAAASUVORK5CYII=\n" } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Visualizing the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A good first-step for many problems is to visualize the data using one of the\n", "*Dimensionality Reduction* techniques we saw earlier. We'll start with the\n", "most straightforward one, Principal Component Analysis (PCA).\n", "\n", "PCA seeks orthogonal linear combinations of the features which show the greatest\n", "variance, and as such, can help give you a good idea of the structure of the\n", "data set. Here we'll use `RandomizedPCA`, because it's faster for large `N`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.decomposition import RandomizedPCA\n", "pca = RandomizedPCA(n_components=2)\n", "proj = pca.fit_transform(digits.data)" ], "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": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 6, "text": [ "<matplotlib.colorbar.Colorbar instance at 0x10d6c0e18>" ] }, { "output_type": "display_data", "png": 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6kA9UIeCV2x4tiJXTFq0W5SP0bFez/aybUZUoMwxs5ZWmr7ZlBRS+C6XG29S7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AQsWbJEzEGhwtufCrPWCq5AISxK+ClfC7L/7KBgNIkjsblY/ANlxMhR8vyLL0rDRo2ELs8Io98S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} ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see that the digits do cluster fairly well, so we can expect even\n", "a fairly naive classification scheme to do a decent job separating them.\n", "\n", "A weakness of PCA is that it produces a linear dimensionality reduction:\n", "this may miss some interesting relationships in the data. If we want to\n", "see a nonlinear mapping of the data, we can use one of the several\n", "methods in the `manifold` module. Here we'll use Isomap (a concatenation\n", "of Isometric Mapping) which is a manifold learning method based on\n", "graph theory:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.manifold import Isomap\n", "iso = Isomap(n_neighbors=5, n_components=2)\n", "proj = iso.fit_transform(digits.data)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python2.7/site-packages/sklearn/neighbors/base.py:327: NeighborsWarning: kneighbors: neighbor k+1 and neighbor k have the same distance: results will be dependent on data order.\n", " return_distance=True)\n" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "<matplotlib.colorbar.Colorbar instance at 0x112679ea8>" ] }, { "output_type": "display_data", "png": 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eHovovvwI9T/T83R1sojdu3dTpHookXG+bJ59kTov5qLGs1EUrxfKq98Ux7xm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qAAAg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\nRvrxuyHU1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} ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be fun to explore the various manifold learning methods available,\n", "and how the output depends on the various parameters used to tune the\n", "projection.\n", "In any case, these visualizations show us that there is hope: even a simple\n", "classifier should be able to adequately identify the members of the various\n", "classes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question: Given these projections of the data, which numbers do you think\n", "a classifier might have trouble distinguishing?**" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Gaussian Naive Bayes Classification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For most classification problems, it's nice to have a simple, fast, go-to\n", "method to provide a quick baseline classification. If the simple and fast\n", "method is sufficient, then we don't have to waste CPU cycles on more complex\n", "models. If not, we can use the results of the simple method to give us\n", "clues about our data.\n", "\n", "One good method to keep in mind is Gaussian Naive Bayes. It is a *generative*\n", "classifier which fits an axis-aligned multi-dimensional Gaussian distribution to\n", "each training label, and uses this to quickly give a rough classification. It\n", "is generally not sufficiently accurate for real-world data, but can perform surprisingly well." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.naive_bayes import GaussianNB\n", "from sklearn.cross_validation import train_test_split" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# split the data into training and validation sets\n", "X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target)\n", "\n", "# train the model\n", "clf = GaussianNB()\n", "clf.fit(X_train, y_train)\n", "\n", "# use the model to predict the labels of the test data\n", "predicted = clf.predict(X_test)\n", "expected = y_test" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question**: why did we split the data into training and validation sets?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the digits again with the predicted labels to get an idea of\n", "how well the classification is working:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", "\n", "# plot the digits: each image is 8x8 pixels\n", "for i in range(64):\n", " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", " ax.imshow(X_test.reshape(-1, 8, 8)[i], cmap=plt.cm.binary,\n", " interpolation='nearest')\n", " \n", " # label the image with the target value\n", " if predicted[i] == expected[i]:\n", " ax.text(0, 7, str(predicted[i]), color='green')\n", " else:\n", " ax.text(0, 7, str(predicted[i]), color='red')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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fnPsCi15fhK5QF7pCXfiHSf+A2793u9th2WbuK3Nx+vxpxMXEYc3da5DQP8Ht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\nu8Vb11lWUhY+fCS6lUOiJW9kHvYu3ut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} ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Quantitative Measurement of Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'd like to measure the performance of our estimator without having to resort\n", "to plotting examples. A simple method might be to simply compare the number of\n", "matches:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "matches = (predicted == expected)\n", "print matches.sum()\n", "print len(matches)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "357\n", "450\n" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "matches.sum() / float(len(matches))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 13, "text": [ "0.79333333333333333" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that nearly 1500 of the 1800 predictions match the input. But there are other\n", "more sophisticated metrics that can be used to judge the performance of a classifier:\n", "several are available in the ``sklearn.metrics`` submodule.\n", "\n", "One of the most useful metrics is the ``classification_report``, which combines several\n", "measures and prints a table with the results:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import metrics\n", "print metrics.classification_report(expected, predicted)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " precision recall f1-score support\n", "\n", " 0 1.00 0.98 0.99 46\n", " 1 0.78 0.83 0.80 46\n", " 2 1.00 0.53 0.69 49\n", " 3 1.00 0.49 0.66 47\n", " 4 0.97 0.80 0.88 44\n", " 5 0.87 0.91 0.89 45\n", " 6 0.95 1.00 0.97 38\n", " 7 0.70 0.98 0.82 51\n", " 8 0.40 0.82 0.54 39\n", " 9 0.88 0.64 0.74 45\n", "\n", "avg / total 0.86 0.79 0.80 450\n", "\n" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another enlightening metric for this sort of multi-label classification\n", "is a *confusion matrix*: it helps us visualize which labels are\n", "being interchanged in the classification errors:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print metrics.confusion_matrix(expected, predicted)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[45 0 0 0 0 0 0 1 0 0]\n", " [ 0 38 0 0 0 0 0 3 3 2]\n", " [ 0 4 26 0 0 1 0 0 18 0]\n", " [ 0 0 0 23 0 2 0 2 18 2]\n", " [ 0 0 0 0 35 0 1 7 1 0]\n", " [ 0 0 0 0 0 41 0 4 0 0]\n", " [ 0 0 0 0 0 0 38 0 0 0]\n", " [ 0 0 0 0 0 1 0 50 0 0]\n", " [ 0 3 0 0 0 2 0 2 32 0]\n", " [ 0 4 0 0 1 0 1 2 8 29]]\n" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see here that in particular, the numbers 1, 2, 3, and 9 are often being labeled 8." ] } ], "metadata": {} } ] }