{ "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": 22, "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": 48, "metadata": {}, "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": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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x7JHr6u1wK/ZvZ+kfrmLO375p1x1O0pCJhHId6M5IUkZODbpesH4RG/71AL6q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\nXja6w8m4258iedjEurotEBDlUT9+kNX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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": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# naive implementation of a Perceptron\n", "\n", "# train a perceptron\n", "def perc(X, y, theta=0.5):\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", " # TODO: find a better way:\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", " \n", " eta = 0.1 # TODO: try with a variable rate\n", " k = 0\n", " grad = 2*theta\n", " while np.abs(grad) > theta:\n", " grad_v = np.zeros(d+1) # the gradient vector\n", " for i in np.arange(n):\n", " # TODO: write the update step\n", " # ...........\n", " pass\n", " \n", " grad = #........... TODO write the normalization of the gradient\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": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1\n", "2\n", "3\n", "4\n", "5\n", "Error rate: 0.333333333333\n" ] }, { "data": { "image/png": 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TJsIVY925r6fKr8JYKVtGe4llQ+dmrjoqrB/v4PLxbs94NsY7PY9HKjRD9cpv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\nk2/Haaq5pcLRGVM5ltzNktL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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": 26, "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": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error rate: 0.058\n", "[[ 5.79398506 0.15191964]]\n", "[ 1.]\n", "[ 1. 5.79398506 0.15191964]\n" ] }, { "data": { "image/png": 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BtUa4fA5rx59E7eQzSOqrNgR0CWBDMRYozesNpkckVAxfM2Rm0UuOHEkgjGE2PDt/zkOQ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\nLRbcA8Gf3wOvZcwBkBCoHrgG4dIZxLV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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": 50, "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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f0d3tZt26r7Nlyyp++tNv9T1fLBdQdnYJweBL+HzbCQb3kJ2tziAnkMJyes8v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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 }