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# `sklearn.metrics.pairwise`.additive_chi2_kernel

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

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

      A feature array.

    Y array-like of shape (n_samples_Y, n_features), default=None

      An optional second feature array. If `None`, uses `Y=X`.

  Returns:
    kernel_matrix ndarray 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