86 lines
3.0 KiB
Python
86 lines
3.0 KiB
Python
"""
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=================================
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Gaussian Mixture Model Ellipsoids
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=================================
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Plot the confidence ellipsoids of a mixture of two Gaussians with EM
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and variational Dirichlet process.
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Both models have access to five components with which to fit the
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data. Note that the EM model will necessarily use all five components
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while the DP model will effectively only use as many as are needed for
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a good fit. This is a property of the Dirichlet Process prior. Here we
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can see that the EM model splits some components arbitrarily, because it
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is trying to fit too many components, while the Dirichlet Process model
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adapts it number of state automatically.
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This example doesn't show it, as we're in a low-dimensional space, but
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another advantage of the Dirichlet process model is that it can fit
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full covariance matrices effectively even when there are less examples
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per cluster than there are dimensions in the data, due to
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regularization properties of the inference algorithm.
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"""
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import itertools
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import numpy as np
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from scipy import linalg
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import matplotlib.pyplot as plt
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import matplotlib as mpl
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from sklearn import mixture
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color_iter = itertools.cycle(['navy', 'c', 'cornflowerblue', 'gold',
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'darkorange'])
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def plot_results(X, Y_, means, covariances, index, title):
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splot = plt.subplot(2, 1, 1 + index)
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for i, (mean, covar, color) in enumerate(zip(
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means, covariances, color_iter)):
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v, w = linalg.eigh(covar)
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v = 2. * np.sqrt(2.) * np.sqrt(v)
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u = w[0] / linalg.norm(w[0])
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# as the DP will not use every component it has access to
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# unless it needs it, we shouldn't plot the redundant
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# components.
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if not np.any(Y_ == i):
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continue
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plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], .8, color=color)
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# Plot an ellipse to show the Gaussian component
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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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ell = mpl.patches.Ellipse(mean, v[0], v[1], 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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plt.xlim(-10., 10.)
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plt.ylim(-3., 6.)
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plt.xticks(())
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plt.yticks(())
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plt.title(title)
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# Number of samples per component
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n_samples = 500
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# Generate random sample, two components
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np.random.seed(0)
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C = np.array([[0., -0.1], [1.7, .4]])
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X = np.r_[np.dot(np.random.randn(n_samples, 2), C),
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.7 * np.random.randn(n_samples, 2) + np.array([-6, 3])]
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# Fit a Gaussian mixture with EM using five components
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gmm = mixture.GaussianMixture(n_components=5, covariance_type='full').fit(X)
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plot_results(X, gmm.predict(X), gmm.means_, gmm.covariances_, 0,
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'Gaussian Mixture')
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# Fit a Dirichlet process Gaussian mixture using five components
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dpgmm = mixture.DPGMM(n_components=5, covariance_type='full').fit(X)
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plot_results(X, dpgmm.predict(X), dpgmm.means_, dpgmm._get_covars(), 1,
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'Dirichlet Process GMM')
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plt.show()
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