pyriemann.utils.mean.mean_power¶

pyriemann.utils.mean.mean_power(X, p, *, sample_weight=None, zeta=1e-09, maxiter=100, init=None)¶

Power mean of SPD/HPD matrices.

Power mean of order \(p\) is the solution of [1] [2]:

\[\mathbf{M} = \sum_i w_i \ \mathbf{M} \sharp_p \mathbf{X}_i\]

where \(\mathbf{A} \sharp_p \mathbf{B}\) is the geodesic between matrices \(\mathbf{A}\) and \(\mathbf{B}\).

Parameters:

Xndarray, shape (n_matrices, n, n): Set of SPD/HPD matrices.
pfloat: Exponent, in [-1,+1]. For p=0, it returns pyriemann.utils.mean.mean_riemann().
sample_weightNone | ndarray, shape (n_matrices,), default=None: Weights for each matrix. If None, it uses equal weights.
zetafloat, default=10e-10: Stopping criterion.
maxiterint, default=100: Maximum number of iterations.
initNone | ndarray, shape (n, n), default=None: A SPD/HPD matrix used to initialize the gradient descent. If None, the weighted power Euclidean mean is used.

Returns: