pyriemann.utils.mean.mean_power

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

The maximum number of iterations.

Returns:

Mndarray, shape (n, n)

Power mean.

See also

mean_covariance

Notes

New in version 0.3.

References

[1]

Matrix Power means and the Karcher mean Y. Lim and M. Palfia. Journal of Functional Analysis, Volume 262, Issue 4, 15 February 2012, Pages 1498-1514.

[2]

Fixed Point Algorithms for Estimating Power Means of Positive Definite Matrices M. Congedo, A. Barachant, and R. Bhatia. IEEE Transactions on Signal Processing, Volume 65, Issue 9, pp.2211-2220, May 2017