additive_chi2_kernel#
- sklearn.metrics.pairwise.additive_chi2_kernel(X,Y=None)[source]#
Compute the additive chi-squared kernel between observations in X and Y.
The chi-squared kernel is computed between each pair of rows in X and Y. Xand Y have to be non-negative. This kernel is most commonly applied tohistograms.
The chi-squared kernel is given by:
k(x, y) = -Sum [(x - y)^2 / (x + y)]
It can be interpreted as a weighted difference per entry.
Read more in theUser Guide.
- Parameters:
- Xarray-like of shape (n_samples_X, n_features)
A feature array.
- Yarray-like of shape (n_samples_Y, n_features), default=None
An optional second feature array. If
None, usesY=X.
- Returns:
- kernelarray-like of shape (n_samples_X, n_samples_Y)
The kernel matrix.
See also
chi2_kernelThe exponentiated version of the kernel, which is usually preferable.
sklearn.kernel_approximation.AdditiveChi2SamplerA Fourier approximation to this kernel.
Notes
As the negative of a distance, this kernel is only conditionally positivedefinite.
References
Zhang, J. and Marszalek, M. and Lazebnik, S. and Schmid, C.Local features and kernels for classification of texture and objectcategories: A comprehensive studyInternational Journal of Computer Vision 2007https://hal.archives-ouvertes.fr/hal-00171412/document
Examples
>>>fromsklearn.metrics.pairwiseimportadditive_chi2_kernel>>>X=[[0,0,0],[1,1,1]]>>>Y=[[1,0,0],[1,1,0]]>>>additive_chi2_kernel(X,Y)array([[-1., -2.], [-2., -1.]])