pyriemann.utils.ajd.ajd_pham¶

pyriemann.utils.ajd.ajd_pham(X, *, init=None, eps=1e-06, n_iter_max=20, sample_weight=None)¶

Approximate joint diagonalization based on Pham’s algorithm.

This is a direct implementation of the AJD algorithm [1], optimizing a log-likelihood criterion based on the Kullback-Leibler divergence.

Parameters:

Xndarray, shape (n_matrices, n, n): Set of SPD/HPD matrices to diagonalize.
initNone | ndarray, shape (n, n), default=None: Initialization for the diagonalizer.
epsfloat, default=1e-6: Tolerance for stoping criterion.
n_iter_maxint, default=20: The maximum number of iterations to reach convergence.
sample_weightNone | ndarray, shape (n_matrices,), default=None: Weights for each matrix, strictly positive. If None, it uses equal weights.

Returns:

Vndarray, shape (n, n): The diagonalizer, an invertible matrix.
Dndarray, shape (n_matrices, n, n): Set of quasi diagonal matrices, D = V X V^H.