.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/svm/plot_svm_tie_breaking.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_svm_plot_svm_tie_breaking.py>`
        to download the full example code. or to run this example in your browser via JupyterLite or Binder

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

.. _sphx_glr_auto_examples_svm_plot_svm_tie_breaking.py:


=========================================================
SVM Tie Breaking Example
=========================================================
Tie breaking is costly if ``decision_function_shape='ovr'``, and therefore it
is not enabled by default. This example illustrates the effect of the
``break_ties`` parameter for a multiclass classification problem and
``decision_function_shape='ovr'``.

The two plots differ only in the area in the middle where the classes are
tied. If ``break_ties=False``, all input in that area would be classified as
one class, whereas if ``break_ties=True``, the tie-breaking mechanism will
create a non-convex decision boundary in that area.

.. GENERATED FROM PYTHON SOURCE LINES 16-67



.. image-sg:: /auto_examples/svm/images/sphx_glr_plot_svm_tie_breaking_001.png
   :alt: break_ties = False, break_ties = True
   :srcset: /auto_examples/svm/images/sphx_glr_plot_svm_tie_breaking_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


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

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import make_blobs
    from sklearn.svm import SVC

    X, y = make_blobs(random_state=27)

    fig, sub = plt.subplots(2, 1, figsize=(5, 8))
    titles = ("break_ties = False", "break_ties = True")

    for break_ties, title, ax in zip((False, True), titles, sub.flatten()):
        svm = SVC(
            kernel="linear", C=1, break_ties=break_ties, decision_function_shape="ovr"
        ).fit(X, y)

        xlim = [X[:, 0].min(), X[:, 0].max()]
        ylim = [X[:, 1].min(), X[:, 1].max()]

        xs = np.linspace(xlim[0], xlim[1], 1000)
        ys = np.linspace(ylim[0], ylim[1], 1000)
        xx, yy = np.meshgrid(xs, ys)

        pred = svm.predict(np.c_[xx.ravel(), yy.ravel()])

        colors = [plt.cm.Accent(i) for i in [0, 4, 7]]

        points = ax.scatter(X[:, 0], X[:, 1], c=y, cmap="Accent")
        classes = [(0, 1), (0, 2), (1, 2)]
        line = np.linspace(X[:, 1].min() - 5, X[:, 1].max() + 5)
        ax.imshow(
            -pred.reshape(xx.shape),
            cmap="Accent",
            alpha=0.2,
            extent=(xlim[0], xlim[1], ylim[1], ylim[0]),
        )

        for coef, intercept, col in zip(svm.coef_, svm.intercept_, classes):
            line2 = -(line * coef[1] + intercept) / coef[0]
            ax.plot(line2, line, "-", c=colors[col[0]])
            ax.plot(line2, line, "--", c=colors[col[1]])
        ax.set_xlim(xlim)
        ax.set_ylim(ylim)
        ax.set_title(title)
        ax.set_aspect("equal")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.903 seconds)


.. _sphx_glr_download_auto_examples_svm_plot_svm_tie_breaking.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/1.6.X?urlpath=lab/tree/notebooks/auto_examples/svm/plot_svm_tie_breaking.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/svm/plot_svm_tie_breaking.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_svm_tie_breaking.recommendations


.. only:: html

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

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