pyriemann.utils.kernel.kernel_riemann¶

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

Affine-invariant Riemannian kernel between two sets of SPD matrices.

Calculates the affine-invariant Riemannian kernel matrix K of inner products of two sets X and Y of SPD matrices on tangent space of Cref by calculating pairwise [1]:

\[K_{i,j} = \text{tr}(\log(C_\text{ref}^{-1/2} X_i C_\text{ref}^{-1/2}) \log(C_\text{ref}^{-1/2} Y_j C_\text{ref}^{-1/2}) )\]

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.
CrefNone | ndarray, shape (n_channels, n_channels), default=None: Reference point for the tangent space and inner product calculation. If None, Cref is calculated as the Riemannian mean of 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 affine-invariant Riemannian kernel matrix between X and Y.