sklearn.metrics.pairwise.additive_chi2_kernel

sklearn.metrics.pairwise.additive_chi2_kernel(X, Y=None)

Computes 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. X and Y have to be non-negative. This kernel is most commonly applied to histograms.

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.

Parameters:

X : array-like of shape (n_samples_X, n_features)

Y : array of shape (n_samples_Y, n_features)

Returns:

kernel_matrix : array of shape (n_samples_X, n_samples_Y)

See also

chi2_kernel

The exponentiated version of the kernel, which is usually preferable.

sklearn.kernel_approximation.AdditiveChi2Sampler

A Fourier approximation to this kernel.

Notes

As the negative of a distance, this kernel is only conditionally positive definite.

References

• Zhang, J. and Marszalek, M. and Lazebnik, S. and Schmid, C. Local features and kernels for classification of texture and object categories: A comprehensive study International Journal of Computer Vision 2007 http://eprints.pascal-network.org/archive/00002309/01/Zhang06-IJCV.pdf