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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_mixture_plot_gmm_selection.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_selection.py:


================================
Gaussian Mixture Model Selection
================================

This example shows that model selection can be performed with
Gaussian Mixture Models using information-theoretic criteria (BIC).
Model selection concerns both the covariance type
and the number of components in the model.
In that case, AIC also provides the right result (not shown to save time),
but BIC is better suited if the problem is to identify the right model.
Unlike Bayesian procedures, such inferences are prior-free.

In that case, the model with 2 components and full covariance
(which corresponds to the true generative model) is selected.

.. GENERATED FROM PYTHON SOURCE LINES 17-101



.. image:: /auto_examples/mixture/images/sphx_glr_plot_gmm_selection_001.png
    :alt: BIC score per model, Selected GMM: full model, 2 components
    :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import itertools

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

    from sklearn import mixture

    print(__doc__)

    # Number of samples per component
    n_samples = 500

    # Generate random sample, two components
    np.random.seed(0)
    C = np.array([[0., -0.1], [1.7, .4]])
    X = np.r_[np.dot(np.random.randn(n_samples, 2), C),
              .7 * np.random.randn(n_samples, 2) + np.array([-6, 3])]

    lowest_bic = np.infty
    bic = []
    n_components_range = range(1, 7)
    cv_types = ['spherical', 'tied', 'diag', 'full']
    for cv_type in cv_types:
        for n_components in n_components_range:
            # Fit a Gaussian mixture with EM
            gmm = mixture.GaussianMixture(n_components=n_components,
                                          covariance_type=cv_type)
            gmm.fit(X)
            bic.append(gmm.bic(X))
            if bic[-1] < lowest_bic:
                lowest_bic = bic[-1]
                best_gmm = gmm

    bic = np.array(bic)
    color_iter = itertools.cycle(['navy', 'turquoise', 'cornflowerblue',
                                  'darkorange'])
    clf = best_gmm
    bars = []

    # Plot the BIC scores
    plt.figure(figsize=(8, 6))
    spl = plt.subplot(2, 1, 1)
    for i, (cv_type, color) in enumerate(zip(cv_types, color_iter)):
        xpos = np.array(n_components_range) + .2 * (i - 2)
        bars.append(plt.bar(xpos, bic[i * len(n_components_range):
                                      (i + 1) * len(n_components_range)],
                            width=.2, color=color))
    plt.xticks(n_components_range)
    plt.ylim([bic.min() * 1.01 - .01 * bic.max(), bic.max()])
    plt.title('BIC score per model')
    xpos = np.mod(bic.argmin(), len(n_components_range)) + .65 +\
        .2 * np.floor(bic.argmin() / len(n_components_range))
    plt.text(xpos, bic.min() * 0.97 + .03 * bic.max(), '*', fontsize=14)
    spl.set_xlabel('Number of components')
    spl.legend([b[0] for b in bars], cv_types)

    # Plot the winner
    splot = plt.subplot(2, 1, 2)
    Y_ = clf.predict(X)
    for i, (mean, cov, color) in enumerate(zip(clf.means_, clf.covariances_,
                                               color_iter)):
        v, w = linalg.eigh(cov)
        if not np.any(Y_ == i):
            continue
        plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], .8, color=color)

        # Plot an ellipse to show the Gaussian component
        angle = np.arctan2(w[0][1], w[0][0])
        angle = 180. * angle / np.pi  # convert to degrees
        v = 2. * np.sqrt(2.) * np.sqrt(v)
        ell = mpl.patches.Ellipse(mean, v[0], v[1], 180. + angle, color=color)
        ell.set_clip_box(splot.bbox)
        ell.set_alpha(.5)
        splot.add_artist(ell)

    plt.xticks(())
    plt.yticks(())
    plt.title(f'Selected GMM: {best_gmm.covariance_type} model, '
              f'{best_gmm.n_components} components')
    plt.subplots_adjust(hspace=.35, bottom=.02)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  1.876 seconds)


.. _sphx_glr_download_auto_examples_mixture_plot_gmm_selection.py:


.. only :: html

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


  .. container:: binder-badge

    .. image:: images/binder_badge_logo.svg
      :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.24.X?urlpath=lab/tree/notebooks/auto_examples/mixture/plot_gmm_selection.ipynb
      :alt: Launch binder
      :width: 150 px


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

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



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

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


.. only:: html

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

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