.. 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

        Click :ref:`here <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 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 12-59



.. image:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpc_xor_001.png
    :alt: 316**2 * RBF(length_scale=1.25)  Log-Marginal-Likelihood:-23.674, 316**2 * DotProduct(sigma_0=0.0104) ** 2  Log-Marginal-Likelihood:-9.284
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    /home/circleci/project/sklearn/gaussian_process/kernels.py:411: 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.
      warnings.warn("The optimal value found for "
    /home/circleci/project/sklearn/gaussian_process/kernels.py:411: 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.
      warnings.warn("The optimal value found for "






|

.. code-block:: default

    print(__doc__)

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

    import numpy as np
    import matplotlib.pyplot as plt

    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=1.0), 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  0.516 seconds)


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


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

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



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

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


.. only:: html

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

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