pyriemann.utils.mean.mean_chol

pyriemann.utils.mean.mean_chol(X, sample_weight=None)

Mean of SPD/HPD matrices according to the Cholesky metric.

Cholesky mean \(\mathbf{M}\) is \(\mathbf{M} = \mathbf{L} \mathbf{L}^H\), where \(\mathbf{L}\) is computed as [1]:

\[\mathbf{L} = \sum_i w_i \text{chol}(\mathbf{X}_i)\]

Parameters:

Xndarray, shape (n_matrices, n, n)

Set of SPD/HPD matrices.

sample_weightNone | ndarray, shape (n_matrices,), default=None

Weights for each matrix. If None, it uses equal weights.

Returns:

Mndarray, shape (n, n)

Cholesky mean.

See also

mean_covariance

Notes

Added in version 0.10.

References

[1]

Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging I.L. Dryden, A. Koloydenko, D. Zhou. Ann Appl Stat, 2009, 3(3), pp. 1102-1123.