pyriemann.utils.mean.mean_power¶
- pyriemann.utils.mean.mean_power(covmats, p, *, sample_weight=None, zeta=1e-09, maxiter=100)¶
Power mean of SPD/HPD matrices.
Power mean of order p is the solution of [1] [2]:
\[\mathbf{C} = \sum_i w_i \ \mathbf{C} \sharp_p \mathbf{X}_i\]where \(\mathbf{A} \sharp_p \mathbf{B}\) is the geodesic between matrices \(\mathbf{A}\) and \(\mathbf{B}\).
- Parameters:
- covmatsndarray, 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:
- Cndarray, shape (n, n)
Power mean.
See also
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