94 lines
3.1 KiB
Python
94 lines
3.1 KiB
Python
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"""
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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
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obtained with Expectation Maximisation (``GaussianMixture`` class) and
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Variational Inference (``BayesianGaussianMixture`` class models with
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a Dirichlet process prior).
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Both models have access to five components with which to fit the data. Note
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that the Expectation Maximisation model will necessarily use all five
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components while the Variational Inference model will effectively only use as
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many as are needed for a good fit. Here we can see that the Expectation
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Maximisation model splits some components arbitrarily, because it is trying to
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fit too many components, while the Dirichlet Process model adapts it number of
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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 matplotlib as mpl
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy import linalg
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from sklearn import mixture
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color_iter = itertools.cycle(["navy", "c", "cornflowerblue", "gold", "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(means, covariances, color_iter)):
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v, w = linalg.eigh(covar)
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v = 2.0 * np.sqrt(2.0) * 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], 0.8, 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 = 180.0 * angle / np.pi # convert to degrees
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ell = mpl.patches.Ellipse(mean, v[0], v[1], angle=180.0 + 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(-9.0, 5.0)
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plt.ylim(-3.0, 6.0)
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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, -0.1], [1.7, 0.4]])
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X = np.r_[
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np.dot(np.random.randn(n_samples, 2), C),
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0.7 * np.random.randn(n_samples, 2) + np.array([-6, 3]),
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]
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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, "Gaussian Mixture")
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# Fit a Dirichlet process Gaussian mixture using five components
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dpgmm = mixture.BayesianGaussianMixture(n_components=5, covariance_type="full").fit(X)
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plot_results(
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X,
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dpgmm.predict(X),
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dpgmm.means_,
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dpgmm.covariances_,
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1,
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"Bayesian Gaussian Mixture with a Dirichlet process prior",
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)
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plt.show()
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