.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` 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.
.. 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
.. code-block:: default
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=[0.5], 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 0.397 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:: https://mybinder.org/badge_logo.svg
:target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.23.X?urlpath=lab/tree/notebooks/auto_examples/gaussian_process/plot_gpc_xor.ipynb
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_gpc_xor.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_gpc_xor.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_