pyriemann.utils.kernel.kernel_logeuclid

pyriemann.utils.kernel.kernel_logeuclid(X, Y=None, *, reg=1e-10, **kwargs)

Log-Euclidean kernel between two sets of SPD matrices.

Calculates the Log-Euclidean kernel matrix \(\mathbf{K}\) of inner products of two sets \(\mathbf{X}\) and \(\mathbf{Y}\) of SPD matrices in \(\mathbb{R}^{n \times n}\) by calculating pairwise products [1]:

\[\mathbf{K}_{i,j} = \text{tr}(\log(\mathbf{X}_i) \log(\mathbf{Y}_j))\]

Parameters:

Xndarray, shape (n_matrices_X, n, n)

First set of SPD matrices.

YNone | ndarray, shape (n_matrices_Y, n, n), default=None

Second set of SPD matrices. If None, Y is set to X.

regfloat, default=1e-10

Regularization parameter to mitigate numerical errors in kernel matrix estimation.

Returns:

Kndarray, shape (n_matrices_X, n_matrices_Y)

The Log-Euclidean kernel matrix between X and Y.

See also

kernel

Notes

New in version 0.3.

References

[1]

Classification of covariance matrices using a Riemannian-based kernel for BCI applications A. Barachant, S. Bonnet, M. Congedo and C. Jutten. Neurocomputing, Elsevier, 2013, 112, pp.172-178.