{ "metadata": { "name": "" }, "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": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# copied from notebook 02_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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3H9rb23HHHXegv78fr7zyCtLS0pyMLakikQgmTZrkdhi2qqioQFlZGQoKChCL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\nm0oQDofjbteKOQ+X6SnadZH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4jBSjtu6YHeuEGWEmFi25RfuCWvoyXOsDTpDapX2BXldX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\n", "text": [ "" ] } ], "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": [], "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": [ "" ] }, { "output_type": "display_data", "png": 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C3DoIXZhiWKJzrkGDG6Jn2xbWW3kzSolC0RYUjkWKM0o9m2HpGtbekbR6YTms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\n6/nIlHs1ktzRQD9nKeI/7Q5MRWKWR/TjIhDX1K3AZBo0qMapU5HYbPcAC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"text": [ "" ] } ], "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." ] }, { "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 fits a Gaussian distribution to each training label independantly on each feature, and uses this to quickly give a rough classification. It is generally not sufficiently accurate for real-world data, but can perform surprisingly well, for instance on text data." ] }, { "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": 5 }, { "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": 6 }, { "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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j27Zt4j7pmtDul076LJ2xKN3jtGtMykrV7s9aKUeT93V+4yMiokDhxEdERIHC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\nGsvt2vh1g5Mi4JkqHM5vfEREFCic+Ii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"text": [ "" ] } ], "prompt_number": 7 }, { "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": [ "365\n", "450\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "matches.sum() / float(len(matches))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 11, "text": [ "0.81111111111111112" ] } ], "prompt_number": 9 }, { "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 1.00 1.00 46\n", " 1 0.75 0.67 0.71 49\n", " 2 0.90 0.45 0.60 42\n", " 3 0.83 0.80 0.81 54\n", " 4 0.98 0.80 0.88 54\n", " 5 0.92 0.89 0.90 37\n", " 6 0.93 0.97 0.95 39\n", " 7 0.69 1.00 0.81 44\n", " 8 0.56 0.88 0.68 49\n", " 9 0.92 0.64 0.75 36\n", "\n", "avg / total 0.84 0.81 0.81 450\n", "\n" ] } ], "prompt_number": 10 }, { "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": [ "[[46 0 0 0 0 0 0 0 0 0]\n", " [ 0 33 0 0 0 0 1 4 10 1]\n", " [ 0 5 19 4 0 0 0 0 14 0]\n", " [ 0 2 1 43 0 2 0 2 3 1]\n", " [ 0 0 0 0 43 0 1 9 1 0]\n", " [ 0 0 0 1 0 33 1 1 1 0]\n", " [ 0 0 1 0 0 0 38 0 0 0]\n", " [ 0 0 0 0 0 0 0 44 0 0]\n", " [ 0 3 0 0 0 1 0 2 43 0]\n", " [ 0 1 0 4 1 0 0 2 5 23]]\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "/home/varoquau/dev/numpy/numpy/core/fromnumeric.py:2499: VisibleDeprecationWarning: `rank` is deprecated; use the `ndim` attribute or function instead. To find the rank of a matrix see `numpy.linalg.matrix_rank`.\n", " VisibleDeprecationWarning)\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see here that in particular, the numbers 1, 2, 3, and 9 are often being labeled 8." ] } ], "metadata": {} } ] }