81 lines
2.6 KiB
Python
81 lines
2.6 KiB
Python
"""
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==============================================================
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Linear Discriminant Analysis & Quadratic Discriminant Analysis
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==============================================================
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Plot the confidence ellipsoids of each class and decision boundary
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"""
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from scipy import linalg
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import numpy as np
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import pylab as pl
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import matplotlib as mpl
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from scikits.learn.lda import LDA
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from scikits.learn.qda import QDA
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################################################################################
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# load sample dataset
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from scikits.learn.datasets import load_iris
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iris = load_iris()
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X = iris.data[:,:2] # Take only 2 dimensions
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y = iris.target
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X = X[y > 0]
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y = y[y > 0]
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y -= 1
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target_names = iris.target_names[1:]
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################################################################################
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# LDA
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lda = LDA()
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y_pred = lda.fit(X, y, store_covariance=True).predict(X)
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# QDA
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qda = QDA()
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y_pred = qda.fit(X, y, store_covariances=True).predict(X)
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###############################################################################
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# Plot results
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def plot_ellipse(splot, mean, cov, color):
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v, w = linalg.eigh(cov)
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u = w[0] / linalg.norm(w[0])
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angle = np.arctan(u[1]/u[0])
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angle = 180 * angle / np.pi # convert to degrees
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# filled gaussian at 2 standard deviation
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ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,
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180 + angle, color=color)
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ell.set_clip_box(splot.bbox)
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ell.set_alpha(0.5)
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splot.add_artist(ell)
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xx, yy = np.meshgrid(np.linspace(4, 8.5, 200), np.linspace(1.5, 4.5, 200))
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X_grid = np.c_[xx.ravel(), yy.ravel()]
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zz_lda = lda.predict_proba(X_grid)[:,1].reshape(xx.shape)
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zz_qda = qda.predict_proba(X_grid)[:,1].reshape(xx.shape)
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pl.figure()
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splot = pl.subplot(1, 2, 1)
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pl.contourf(xx, yy, zz_lda > 0.5, alpha=0.5)
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pl.scatter(X[y==0,0], X[y==0,1], c='b', label=target_names[0])
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pl.scatter(X[y==1,0], X[y==1,1], c='r', label=target_names[1])
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pl.contour(xx, yy, zz_lda, [0.5], linewidths=2., colors='k')
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plot_ellipse(splot, lda.means_[0], lda.covariance_, 'b')
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plot_ellipse(splot, lda.means_[1], lda.covariance_, 'r')
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pl.legend()
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pl.axis('tight')
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pl.title('Linear Discriminant Analysis')
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splot = pl.subplot(1, 2, 2)
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pl.contourf(xx, yy, zz_qda > 0.5, alpha=0.5)
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pl.scatter(X[y==0,0], X[y==0,1], c='b', label=target_names[0])
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pl.scatter(X[y==1,0], X[y==1,1], c='r', label=target_names[1])
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pl.contour(xx, yy, zz_qda, [0.5], linewidths=2., colors='k')
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plot_ellipse(splot, qda.means_[0], qda.covariances_[0], 'b')
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plot_ellipse(splot, qda.means_[1], qda.covariances_[1], 'r')
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pl.legend()
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pl.axis('tight')
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pl.title('Quadratic Discriminant Analysis')
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pl.show()
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