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 K of inner products of two sets X and Y of SPD matrices by calculating pairwise [1]:

\[K_{i,j} = \text{tr}(\log(X_i) \log(Y_j))\]

Parameters

Xndarray, shape (n_matrices_X, n_channels, n_channels): First set of SPD matrices.
YNone | ndarray, shape (n_matrices_Y, n_channels, n_channels), 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.