.. _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. .. image:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpc_xor_001.png :align: center .. code-block:: python print(__doc__) # Authors: Jan Hendrik Metzen # # 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], linewidths=2, linetypes='--') 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() **Total running time of the script:** ( 0 minutes 0.669 seconds) .. container:: sphx-glr-footer .. container:: sphx-glr-download :download:`Download Python source code: plot_gpc_xor.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_gpc_xor.ipynb ` .. rst-class:: sphx-glr-signature `Generated by Sphinx-Gallery `_