sklearn.metrics.pairwise
.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. 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.
Read more in the User 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:
- kernelndarray of shape (n_samples_X, n_samples_Y)
The kernel matrix.
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 https://hal.archives-ouvertes.fr/hal-00171412/document
Examples
>>> from sklearn.metrics.pairwise import additive_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.]])