62 lines
2.1 KiB
Python
62 lines
2.1 KiB
Python
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"""
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========================================================================
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Illustration of Gaussian process classification (GPC) on the XOR dataset
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========================================================================
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This example illustrates GPC on XOR data. Compared are a stationary, isotropic
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kernel (RBF) and a non-stationary kernel (DotProduct). On this particular
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dataset, the DotProduct kernel obtains considerably better results because the
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class-boundaries are linear and coincide with the coordinate axes. In general,
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stationary kernels often obtain better results.
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"""
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# Authors: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
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#
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# License: BSD 3 clause
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.gaussian_process import GaussianProcessClassifier
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from sklearn.gaussian_process.kernels import RBF, DotProduct
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xx, yy = np.meshgrid(np.linspace(-3, 3, 50), np.linspace(-3, 3, 50))
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rng = np.random.RandomState(0)
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X = rng.randn(200, 2)
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Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)
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# fit the model
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plt.figure(figsize=(10, 5))
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kernels = [1.0 * RBF(length_scale=1.15), 1.0 * DotProduct(sigma_0=1.0) ** 2]
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for i, kernel in enumerate(kernels):
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clf = GaussianProcessClassifier(kernel=kernel, warm_start=True).fit(X, Y)
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# plot the decision function for each datapoint on the grid
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Z = clf.predict_proba(np.vstack((xx.ravel(), yy.ravel())).T)[:, 1]
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Z = Z.reshape(xx.shape)
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plt.subplot(1, 2, i + 1)
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image = plt.imshow(
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Z,
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interpolation="nearest",
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extent=(xx.min(), xx.max(), yy.min(), yy.max()),
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aspect="auto",
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origin="lower",
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cmap=plt.cm.PuOr_r,
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)
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contours = plt.contour(xx, yy, Z, levels=[0.5], linewidths=2, colors=["k"])
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plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired, edgecolors=(0, 0, 0))
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plt.xticks(())
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plt.yticks(())
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plt.axis([-3, 3, -3, 3])
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plt.colorbar(image)
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plt.title(
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"%s\n Log-Marginal-Likelihood:%.3f"
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% (clf.kernel_, clf.log_marginal_likelihood(clf.kernel_.theta)),
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fontsize=12,
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)
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plt.tight_layout()
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plt.show()
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