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additive_chi2_kernel — scikit-learn 1.8.dev0 documentation

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, uses Y=X.

Returns:

kernelarray-like of shape (n_samples_X, n_samples_Y)

The kernel matrix.

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.]])

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