pyriemann.utils.mean.mean_alm¶

pyriemann.utils.mean.mean_alm(X, *, tol=1e-14, maxiter=100, sample_weight=None)¶

Ando-Li-Mathias (ALM) mean of SPD/HPD matrices.

Ando-Li-Mathias (ALM) mean is computed recursively, generalizing from [1]:

\[\mathbf{M} = X_1^{\frac{1}{2}} (X_1^{-\frac{1}{2}}X_2^{\frac{1}{2}} X_1^{-\frac{1}{2}})^{\frac{1}{2}} X_1^{\frac{1}{2}}\]

and requiring a high number of iterations. Extremely slow, due to the recursive formulation.

Parameters:

Xndarray, shape (n_matrices, n, n): Set of SPD/HPD matrices.
tolfloat, default=10e-14: Tolerance to stop the gradient descent.
maxiterint, default=100: Maximum number of iterations.
sample_weightNone | ndarray, shape (n_matrices,), default=None: Weights for each matrix. If None, it uses equal weights.

Returns: