{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PR02: Linear discriminants - part 1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "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": 13, "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": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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": 15, "metadata": {}, "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 {:d}\".format(k))\n", " grad = eta * np.linalg.norm(grad_v) # norm\n", " \n", " return a\n", "\n", "\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": 17, "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: 0.333333\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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: {:f}\".format(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": 19, "metadata": {}, "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": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error rate: 0.163000\n", "[[-3.86378782 -0.48746302]]\n", "[-1.]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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: {:f}\".format(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": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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.covariance_[0], 'red')\n", " plot_ellipse(splot, qda.means_[1], qda.covariance_[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_covariance=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 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }