pyriemann.utils.kernel.kernel¶

pyriemann.utils.kernel.kernel(X, Y=None, *, Cref=None, metric='riemann', reg=1e-10)¶

Kernel matrix between matrices according to a specified metric.

It calculates the kernel matrix \(\mathbf{K}\) of pairwise inner products of two sets \(\mathbf{X}\) and \(\mathbf{Y}\) of matrices on the tangent space at \(\mathbf{C}_\text{ref}\), according to a specified metric.

Parameters:

Xndarray, shape (n_matrices_X, n, n): First set of matrices.
YNone | ndarray, shape (n_matrices_Y, n, n), default=None: Second set of matrices. If None, Y is set to X.
CrefNone | ndarray, shape (n, n), default=None: Reference matrix.
metricstring | callable, default=”riemann”: Metric used for tangent space and mean estimation, can be: “euclid”, “logeuclid”, “riemann”, or a callable function.
regfloat, default=1e-10: When Y is None, regularization parameter to mitigate numerical errors in kernel matrix estimation, to provide a positive-definite kernel matrix.

Returns:

Kndarray, shape (n_matrices_X, n_matrices_Y): Kernel matrix between X and Y.