pyriemann.utils.distance.distance_wasserstein

pyriemann.utils.distance.distance_wasserstein(A, B)

Wasserstein distance between SPSD/HPSD matrices.

The Wasserstein distance between two SPSD/HPSD matrices A and B is [1] [2]:

\[d(\mathbf{A},\mathbf{B}) = \sqrt{ \text{tr}(A + B - 2(B^{1/2} A B^{1/2})^{1/2}) }\]

Parameters

Andarray, shape (…, n, n)

First SPSD/HPSD matrices, at least 2D ndarray.

Bndarray, shape (…, n, n)

Second SPSD/HPSD matrices, same dimensions as A.

Returns

dndarray, shape (…,) or float

Wasserstein distance between A and B.

References

1

Optimal transport: old and new C. Villani. Springer Science & Business Media, 2008, vol. 338

2

An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras D. Bures. Trans Am Math Soc, 1969, 135, pp. 199-212