.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gaussian_process/plot_gpc_xor.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_gaussian_process_plot_gpc_xor.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_gaussian_process_plot_gpc_xor.py:


========================================================================
Illustration of Gaussian process classification (GPC) on the XOR dataset
========================================================================

This example illustrates GPC on XOR data. Compared are a stationary, isotropic
kernel (RBF) and a non-stationary kernel (DotProduct). On this particular
dataset, the DotProduct kernel obtains considerably better results because the
class-boundaries are linear and coincide with the coordinate axes. In general,
stationary kernels often obtain better results.

.. GENERATED FROM PYTHON SOURCE LINES 13-62



.. image-sg:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpc_xor_001.png
   :alt: 302**2 * RBF(length_scale=1.55)  Log-Marginal-Likelihood:-24.237, 316**2 * DotProduct(sigma_0=0.0104) ** 2  Log-Marginal-Likelihood:-9.284
   :srcset: /auto_examples/gaussian_process/images/sphx_glr_plot_gpc_xor_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/runner/work/scikit-learn-pst/scikit-learn-pst/sklearn/gaussian_process/kernels.py:455: ConvergenceWarning:

    The optimal value found for dimension 0 of parameter k1__constant_value is close to the specified upper bound 100000.0. Increasing the bound and calling fit again may find a better value.







|

.. code-block:: Python


    # Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
    #
    # License: BSD 3 clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.gaussian_process import GaussianProcessClassifier
    from sklearn.gaussian_process.kernels import RBF, DotProduct

    xx, yy = np.meshgrid(np.linspace(-3, 3, 50), np.linspace(-3, 3, 50))
    rng = np.random.RandomState(0)
    X = rng.randn(200, 2)
    Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)

    # fit the model
    plt.figure(figsize=(10, 5))
    kernels = [1.0 * RBF(length_scale=1.15), 1.0 * DotProduct(sigma_0=1.0) ** 2]
    for i, kernel in enumerate(kernels):
        clf = GaussianProcessClassifier(kernel=kernel, warm_start=True).fit(X, Y)

        # plot the decision function for each datapoint on the grid
        Z = clf.predict_proba(np.vstack((xx.ravel(), yy.ravel())).T)[:, 1]
        Z = Z.reshape(xx.shape)

        plt.subplot(1, 2, i + 1)
        image = plt.imshow(
            Z,
            interpolation="nearest",
            extent=(xx.min(), xx.max(), yy.min(), yy.max()),
            aspect="auto",
            origin="lower",
            cmap=plt.cm.PuOr_r,
        )
        contours = plt.contour(xx, yy, Z, levels=[0.5], linewidths=2, colors=["k"])
        plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired, edgecolors=(0, 0, 0))
        plt.xticks(())
        plt.yticks(())
        plt.axis([-3, 3, -3, 3])
        plt.colorbar(image)
        plt.title(
            "%s\n Log-Marginal-Likelihood:%.3f"
            % (clf.kernel_, clf.log_marginal_likelihood(clf.kernel_.theta)),
            fontsize=12,
        )

    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.749 seconds)


.. _sphx_glr_download_auto_examples_gaussian_process_plot_gpc_xor.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/gaussian_process/plot_gpc_xor.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/gaussian_process/plot_gpc_xor.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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


.. include:: plot_gpc_xor.recommendations


.. only:: html

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

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