.. _sphx_glr_auto_examples_decomposition_plot_beta_divergence.py:


==============================
Beta-divergence loss functions
==============================

A plot that compares the various Beta-divergence loss functions supported by
the Multiplicative-Update ('mu') solver in :class:`sklearn.decomposition.NMF`.




.. image:: /auto_examples/decomposition/images/sphx_glr_plot_beta_divergence_001.png
    :align: center





.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from sklearn.decomposition.nmf import _beta_divergence

    print(__doc__)

    x = np.linspace(0.001, 4, 1000)
    y = np.zeros(x.shape)

    colors = 'mbgyr'
    for j, beta in enumerate((0., 0.5, 1., 1.5, 2.)):
        for i, xi in enumerate(x):
            y[i] = _beta_divergence(1, xi, 1, beta)
        name = "beta = %1.1f" % beta
        plt.plot(x, y, label=name, color=colors[j])

    plt.xlabel("x")
    plt.title("beta-divergence(1, x)")
    plt.legend(loc=0)
    plt.axis([0, 4, 0, 3])
    plt.show()

**Total running time of the script:** ( 0 minutes  0.357 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

    `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_