{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PR02: Linear discriminants - part 1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from sklearn import datasets\n", "from sklearn import metrics\n", "\n", "from matplotlib import pylab as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate a binary classification problem" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X0, y0 = datasets.make_classification(1000, n_features=2, weights=[0.4,0.6],\n", " n_informative=2, n_redundant=0, \n", " n_clusters_per_class=1, flip_y=0.01,\n", " shuffle=True)\n", "y0[y0 == 0] = -1" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YxZmllDjjU2jyFUUMJVTsDlP6VtdMl5PNjhAKY/70r2A90S5DJhDbLZv6ok0R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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the data points - just to see how the classes look like\n", "plt.scatter(X0[:,0], X0[:,1], c=y0, cmap=plt.cm.Paired)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Perceptron" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, try your own implementation of the Perceptron algorithm. For example, fill in the gaps below:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# naive implementation of a Perceptron\n", "\n", "# train a perceptron\n", "def perc(X, y, theta=0.5, eta=0.1):\n", " n, d = X.shape # n samples, d variables\n", " a = np.ones(d+1) # a = [1,....,1]\n", " Z = np.zeros((n, d+1))\n", " \n", " for i in np.arange(n):\n", " Z[i, 0] = y[i]\n", " Z[i, 1:(d+1)] = y[i] * X[i,:]\n", "\n", " k = 0\n", " grad = 2*theta\n", " while np.abs(grad) > theta:\n", " grad_v = np.zeros(d+1)\n", " for i in np.arange(n):\n", " if np.dot(a, Z[i,:]) < 0:\n", " # i-th sample is misclassified\n", " a += eta*Z[i,:]\n", " k += 1\n", " grad_v += Z[i,:]\n", " print \"Coefficient update\", k\n", " grad = eta * np.linalg.norm(grad_v) # norm\n", " \n", " return a\n", "\n", "\n", "# use a trained model to classify a new dataset\n", "def perc_clsf(X, a):\n", " d = a[0]\n", " d += np.dot(X, a[1:])\n", " c = np.ones(X.shape[0], dtype=np.int)\n", " c[d < 0] = -1\n", "\n", " return c\n", "\n", "\n", "# show separation boundary\n", "def plot_clsf_reg(X, y, a):\n", " xmn, xmx = X[:,0].min() - 1, X[:,0].max() + 1\n", " ymn, ymx = X[:,1].min() - 1, X[:,1].max() + 1\n", " \n", " xx, yy = np.meshgrid(np.arange(xmn,xmx,0.02), np.arange(ymn,ymx,0.02))\n", " Z = perc_clsf(np.c_[xx.ravel(),yy.ravel()], a)\n", "\n", " # for plotting, convert to 0, 1:\n", " Z = (Z + 1) / 2\n", " Z = Z.reshape(xx.shape)\n", " \n", " plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)\n", "\n", " # add the points with \n", " plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Paired)\n", " plt.xlim(xx.min(), xx.max())\n", " plt.ylim(yy.min(), yy.max())\n", "\n", " plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And apply it to the data generated above or to the classical IRIS dataset:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coefficient update 1\n", "Coefficient update 2\n", "Coefficient update 3\n", "Coefficient update 4\n", "Coefficient update 5\n", "Error rate: 0.333333333333\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 0.7 -0.92 0.16]\n" ] } ], "source": [ "iris = datasets.load_iris()\n", "X = iris.data[:, :2] # we only take the first two features. We could\n", " # avoid this ugly slicing by using a two-dim dataset\n", "y = iris.target\n", "# Just 2 classes...\n", "y[y > 0] = -1\n", "y[y == 0] = 1\n", "\n", "a = perc(X, y)\n", "yy = perc_clsf(X, a) # get the predicted labels...\n", "# ...and compare y to yy (error rate):\n", "print \"Error rate:\", np.sum(y != yy) / float(yy.size)\n", "\n", "# TODO: try\n", "#a = perc(X, y, 0.1)\n", "#a = perc(X, y, 0.05)\n", "\n", "plot_clsf_reg (X, y, a)\n", "print a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the professional way:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.linear_model import Perceptron" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Have a look at [http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Perceptron.html] for documentation of the class. Identify the parameters discussed during the lecture." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/linear_model/stochastic_gradient.py:84: FutureWarning: max_iter and tol parameters have been added in in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.\n", " \"and default tol will be 1e-3.\" % type(self), FutureWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Error rate: 0.13\n", "[[-1.21539495 -0.29874331]]\n", "[ 0.]\n" ] }, { "data": { "image/png": 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fv0L2z39s43lTr2pViSpkL1Gffx/WS96wbrsQAuuZP078b38B4apMICeF9V0/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\nuZWZv+f/+BCABmN0FMMICYHI+HRzFcVu8BdVGzrbkCoXPZp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clsf = Perceptron() # create a default Perceptron classifier. TODO: try different initial parameters\n", "clsf.fit(X0, y0) # train the classifier\n", "yy = clsf.predict(X0) # make predictions. NOTE: usually you predict a new set of points\n", "print \"Error rate:\", np.sum(y0 != yy) / float(yy.size)\n", "print clsf.coef_\n", "print clsf.intercept_\n", "w = np.hstack((clsf.intercept_, clsf.coef_[0,] ))\n", "\n", "plot_clsf_reg (X0, y0, w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### TODO/HOMEWORK\n", "- use numpy.random.shuffle() function, to shuffle your dataset and then re-train the classifier. Does the solution change?\n", "- random partition your data into a \"train set\" and a \"test set\" (e.g. using numpy.random.choice()). Then train a classifier on the \"train set\" and apply it to the \"test set\". How does the test error rate compare with the train error rate?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fisher linear discriminant\n", "- FDA (Fisher discriminant analysis) is LDA (linear discriminant analysis) for 2 classes\n", "- check the documentation for LDA: http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html\n", "- repeat the training/testing/plotting steps from above, but in the case of LDA. \n", "- go through the example below (taken from scikit-learn http://scikit-learn.org/stable/auto_examples/classification/plot_lda_qda.html) and try to understand the principles (not the details):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/discriminant_analysis.py:664: DeprecationWarning: 'store_covariances' was renamed to store_covariance in version 0.19 and will be removed in 0.21.\n", " DeprecationWarning)\n", "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/utils/deprecation.py:75: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/utils/deprecation.py:75: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/discriminant_analysis.py:664: DeprecationWarning: 'store_covariances' was renamed to store_covariance in version 0.19 and will be removed in 0.21.\n", " DeprecationWarning)\n", "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/utils/deprecation.py:75: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n", "/Users/chief/anaconda2/lib/python2.7/site-packages/sklearn/utils/deprecation.py:75: DeprecationWarning: Function covariances_ is deprecated; Attribute covariances_ was deprecated in version 0.19 and will be removed in 0.21. Use covariance_ instead\n", " warnings.warn(msg, category=DeprecationWarning)\n" ] }, { "data": { "image/png": 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IIAkRE5x3vXnuP5/rNo0EZ6OvLhjP43xhCCvPSrR45rioEy2KlRDRSoh45ngcHdGWaA/R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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import linalg\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from matplotlib import colors\n", "\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n", "\n", "# #############################################################################\n", "# Colormap\n", "cmap = colors.LinearSegmentedColormap(\n", " 'red_blue_classes',\n", " {'red': [(0, 1, 1), (1, 0.7, 0.7)],\n", " 'green': [(0, 0.7, 0.7), (1, 0.7, 0.7)],\n", " 'blue': [(0, 0.7, 0.7), (1, 1, 1)]})\n", "plt.cm.register_cmap(cmap=cmap)\n", "\n", "\n", "# #############################################################################\n", "# Generate datasets\n", "def dataset_fixed_cov():\n", " '''Generate 2 Gaussians samples with the same covariance matrix'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -0.23], [0.83, .23]])\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "def dataset_cov():\n", " '''Generate 2 Gaussians samples with different covariance matrices'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -1.], [2.5, .7]]) * 2.\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "# #############################################################################\n", "# Plot functions\n", "def plot_data(lda, X, y, y_pred, fig_index):\n", " splot = plt.subplot(2, 2, fig_index)\n", " if fig_index == 1:\n", " plt.title('Linear Discriminant Analysis')\n", " plt.ylabel('Data with\\n fixed covariance')\n", " elif fig_index == 2:\n", " plt.title('Quadratic Discriminant Analysis')\n", " elif fig_index == 3:\n", " plt.ylabel('Data with\\n varying covariances')\n", "\n", " tp = (y == y_pred) # True Positive\n", " tp0, tp1 = tp[y == 0], tp[y == 1]\n", " X0, X1 = X[y == 0], X[y == 1]\n", " X0_tp, X0_fp = X0[tp0], X0[~tp0]\n", " X1_tp, X1_fp = X1[tp1], X1[~tp1]\n", "\n", " alpha = 0.5\n", "\n", " # class 0: dots\n", " plt.plot(X0_tp[:, 0], X0_tp[:, 1], 'o', alpha=alpha,\n", " color='red', markeredgecolor='k')\n", " plt.plot(X0_fp[:, 0], X0_fp[:, 1], '*', alpha=alpha,\n", " color='#990000', markeredgecolor='k') # dark red\n", "\n", " # class 1: dots\n", " plt.plot(X1_tp[:, 0], X1_tp[:, 1], 'o', alpha=alpha,\n", " color='blue', markeredgecolor='k')\n", " plt.plot(X1_fp[:, 0], X1_fp[:, 1], '*', alpha=alpha,\n", " color='#000099', markeredgecolor='k') # dark blue\n", "\n", " # class 0 and 1 : areas\n", " nx, ny = 200, 100\n", " x_min, x_max = plt.xlim()\n", " y_min, y_max = plt.ylim()\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", " Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z[:, 1].reshape(xx.shape)\n", " plt.pcolormesh(xx, yy, Z, cmap='red_blue_classes',\n", " norm=colors.Normalize(0., 1.))\n", " plt.contour(xx, yy, Z, [0.5], linewidths=2., colors='k')\n", "\n", " # means\n", " plt.plot(lda.means_[0][0], lda.means_[0][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", " plt.plot(lda.means_[1][0], lda.means_[1][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", "\n", " return splot\n", "\n", "\n", "def plot_ellipse(splot, mean, cov, color):\n", " v, w = linalg.eigh(cov)\n", " u = w[0] / linalg.norm(w[0])\n", " angle = np.arctan(u[1] / u[0])\n", " angle = 180 * angle / np.pi # convert to degrees\n", " # filled Gaussian at 2 standard deviation\n", " ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,\n", " 180 + angle, facecolor=color,\n", " edgecolor='yellow',\n", " linewidth=2, zorder=2)\n", " ell.set_clip_box(splot.bbox)\n", " ell.set_alpha(0.5)\n", " splot.add_artist(ell)\n", " splot.set_xticks(())\n", " splot.set_yticks(())\n", "\n", "\n", "def plot_lda_cov(lda, splot):\n", " plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')\n", " plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')\n", "\n", "\n", "def plot_qda_cov(qda, splot):\n", " plot_ellipse(splot, qda.means_[0], qda.covariances_[0], 'red')\n", " plot_ellipse(splot, qda.means_[1], qda.covariances_[1], 'blue')\n", "\n", "for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):\n", " # Linear Discriminant Analysis\n", " lda = LinearDiscriminantAnalysis(solver=\"svd\", store_covariance=True)\n", " y_pred = lda.fit(X, y).predict(X)\n", " splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)\n", " plot_lda_cov(lda, splot)\n", " plt.axis('tight')\n", "\n", " # Quadratic Discriminant Analysis\n", " qda = QuadraticDiscriminantAnalysis(store_covariances=True)\n", " y_pred = qda.fit(X, y).predict(X)\n", " splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)\n", " plot_qda_cov(qda, splot)\n", " plt.axis('tight')\n", "plt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant'\n", " 'Analysis')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }