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

    Click :ref:`here <sphx_glr_download_auto_examples_linear_model_plot_sgd_loss_functions.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_linear_model_plot_sgd_loss_functions.py:


==========================
SGD: convex loss functions
==========================

A plot that compares the various convex loss functions supported by
:class:`sklearn.linear_model.SGDClassifier` .



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_sgd_loss_functions_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none







|


.. code-block:: default

    print(__doc__)

    import numpy as np
    import matplotlib.pyplot as plt


    def modified_huber_loss(y_true, y_pred):
        z = y_pred * y_true
        loss = -4 * z
        loss[z >= -1] = (1 - z[z >= -1]) ** 2
        loss[z >= 1.] = 0
        return loss


    xmin, xmax = -4, 4
    xx = np.linspace(xmin, xmax, 100)
    lw = 2
    plt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color='gold', lw=lw,
             label="Zero-one loss")
    plt.plot(xx, np.where(xx < 1, 1 - xx, 0), color='teal', lw=lw,
             label="Hinge loss")
    plt.plot(xx, -np.minimum(xx, 0), color='yellowgreen', lw=lw,
             label="Perceptron loss")
    plt.plot(xx, np.log2(1 + np.exp(-xx)), color='cornflowerblue', lw=lw,
             label="Log loss")
    plt.plot(xx, np.where(xx < 1, 1 - xx, 0) ** 2, color='orange', lw=lw,
             label="Squared hinge loss")
    plt.plot(xx, modified_huber_loss(xx, 1), color='darkorchid', lw=lw,
             linestyle='--', label="Modified Huber loss")
    plt.ylim((0, 8))
    plt.legend(loc="upper right")
    plt.xlabel(r"Decision function $f(x)$")
    plt.ylabel("$L(y=1, f(x))$")
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.166 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_sgd_loss_functions.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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