Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

Note

Go to the end to download the full example code or to run this example in your browser via Binder

# Gaussian Mixture Model Ellipsoids

Plot the confidence ellipsoids of a mixture of two Gaussians obtained with Expectation Maximisation (`GaussianMixture` class) and Variational Inference (`BayesianGaussianMixture` class models with a Dirichlet process prior).

Both models have access to five components with which to fit the data. Note that the Expectation Maximisation model will necessarily use all five components while the Variational Inference model will effectively only use as many as are needed for a good fit. Here we can see that the Expectation Maximisation model splits some components arbitrarily, because it is trying to fit too many components, while the Dirichlet Process model adapts it number of state automatically.

This example doesn’t show it, as we’re in a low-dimensional space, but another advantage of the Dirichlet process model is that it can fit full covariance matrices effectively even when there are less examples per cluster than there are dimensions in the data, due to regularization properties of the inference algorithm.

    /root/scikit-learn-1.3.2/sklearn/mixture/_base.py:268: ConvergenceWarning:

    Initialization 1 did not converge. Try different init parameters, or increase max_iter, tol or check for degenerate data.

    import itertools

    import matplotlib as mpl
    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import linalg

    from sklearn import mixture

    color_iter = itertools.cycle(["navy", "c", "cornflowerblue", "gold", "darkorange"])

    def plot_results(X, Y_, means, covariances, index, title):
        splot = plt.subplot(2, 1, 1 + index)
        for i, (mean, covar, color) in enumerate(zip(means, covariances, color_iter)):
            v, w = linalg.eigh(covar)
            v = 2.0 * np.sqrt(2.0) * np.sqrt(v)
            u = w[0] / linalg.norm(w[0])
            # as the DP will not use every component it has access to
            # unless it needs it, we shouldn't plot the redundant
            # components.
            if not np.any(Y_ == i):
                continue
            plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], 0.8, color=color)

            # Plot an ellipse to show the Gaussian component
            angle = np.arctan(u[1] / u[0])
            angle = 180.0 * angle / np.pi  # convert to degrees
            ell = mpl.patches.Ellipse(mean, v[0], v[1], angle=180.0 + angle, color=color)
            ell.set_clip_box(splot.bbox)
            ell.set_alpha(0.5)
            splot.add_artist(ell)

        plt.xlim(-9.0, 5.0)
        plt.ylim(-3.0, 6.0)
        plt.xticks(())
        plt.yticks(())
        plt.title(title)

    # Number of samples per component
    n_samples = 500

    # Generate random sample, two components
    np.random.seed(0)
    C = np.array([[0.0, -0.1], [1.7, 0.4]])
    X = np.r_[
        np.dot(np.random.randn(n_samples, 2), C),
        0.7 * np.random.randn(n_samples, 2) + np.array([-6, 3]),
    ]

    # Fit a Gaussian mixture with EM using five components
    gmm = mixture.GaussianMixture(n_components=5, covariance_type="full").fit(X)
    plot_results(X, gmm.predict(X), gmm.means_, gmm.covariances_, 0, "Gaussian Mixture")

    # Fit a Dirichlet process Gaussian mixture using five components
    dpgmm = mixture.BayesianGaussianMixture(n_components=5, covariance_type="full").fit(X)
    plot_results(
        X,
        dpgmm.predict(X),
        dpgmm.means_,
        dpgmm.covariances_,
        1,
        "Bayesian Gaussian Mixture with a Dirichlet process prior",
    )

    plt.show()

Total running time of the script: (0 minutes 0.149 seconds)

Gallery generated by Sphinx-Gallery