.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/mixture/plot_gmm.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_mixture_plot_gmm.py>`
        to download the full example code. or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_mixture_plot_gmm.py:


=================================
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.

.. GENERATED FROM PYTHON SOURCE LINES 26-97



.. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_001.png
   :alt: Gaussian Mixture, Bayesian Gaussian Mixture with a Dirichlet process prior
   :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /opt/hostedtoolcache/Python/3.9.19/x64/lib/python3.9/site-packages/sklearn/mixture/_base.py:269: ConvergenceWarning:

    Best performing initialization did not converge. Try different init parameters, or increase max_iter, tol, or check for degenerate data.







|

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause

    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()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.187 seconds)


.. _sphx_glr_download_auto_examples_mixture_plot_gmm.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/mixture/plot_gmm.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_gmm.ipynb <plot_gmm.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_gmm.py <plot_gmm.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_gmm.zip <plot_gmm.zip>`


.. include:: plot_gmm.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_