- "print(__doc__)\n\nfrom scipy import linalg\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib as mpl\nfrom matplotlib import colors\n\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\nfrom sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n\n# #############################################################################\n# Colormap\ncmap = 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)]})\nplt.cm.register_cmap(cmap=cmap)\n\n\n# #############################################################################\n# Generate datasets\ndef 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\ndef 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\ndef 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\ndef 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\ndef 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\ndef 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\nfor 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')\nplt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant'\n 'Analysis')\nplt.show()"
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