.. 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 ` 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/circleci/project/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 # # 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 0.592 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/1.4.X?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 ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_gpc_xor.py ` .. include:: plot_gpc_xor.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_