spd_learn.functional.mean_kullback_sym#

spd_learn.functional.mean_kullback_sym(X, sample_weight=None, **kwargs)[source]#

Mean of SPD/HPD matrices according to Kullback-Leibler divergence.

Symmetrized Kullback-Leibler mean is the geometric mean between the Euclidean and the harmonic means [1].

Parameters:

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

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

Returns:

M – Symmetrized Kullback-Leibler mean.

Return type:

ndarray, shape (…, n, n)

Notes

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

See also

gmean

References

[1]

Symmetric positive-definite matrices: From geometry to applications and visualization M. Moakher and P. Batchelor. Visualization and Processing of Tensor Fields, pp. 285-298, 2006