spd_learn.functional.mean_poweuclid

spd_learn.functional.mean_poweuclid(X, p, *, sample_weight=None, **kwargs)

Mean of SPD/HPD matrices according to the power Euclidean metric.

Power Euclidean mean of order \(p\) is [1]:

\[\mathbf{M} = \left( \sum_i w_i \ \mathbf{X}_i^p \right)^{1/p}\]

with \(w\) being the weights which sum to 1.

Parameters:

• X (ndarray, shape (..., n_matrices, n, n)) – Set of SPD/HPD matrices.

• p (float) – Exponent.

• sample_weight (None | ndarray, shape (n_matrices,), default=None) – Weights for each matrix. If None, it uses equal weights.

Returns:

M – Power Euclidean mean.

Return type:

ndarray, shape (…, n, n)

Notes

Changed in version 0.12: Add support for NumPy and PyTorch.

See also

gmean

References

[1]

Power Euclidean metrics for covariance matrices with application to diffusion tensor imaging I.L. Dryden, X. Pennec, & J.M. Peyrat. arXiv, 2010.