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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.
/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. warnings.warn(
# Authors: The scikit-learn developers # SPDX-License-Identifier: 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()
Total running time of the script: (0 minutes 0.363 seconds)
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