pyriemann.utils.tangentspace.exp_map_wasserstein

pyriemann.utils.tangentspace.exp_map_wasserstein(X, Cref)

Project matrices back to manifold by Wasserstein exponential map.

The projection of a matrix \(\mathbf{X}\) from tangent space to SPD/HPD manifold with Wasserstein exponential map according to a reference SPD/HPD matrix \(\mathbf{C}_\text{ref}\) is given in Eq.(36) of [1].

Parameters:

Xndarray, shape (…, n, n)

Matrices in tangent space.

Crefndarray, shape (n, n)

Reference SPD/HPD matrix.

Returns:

X_originalndarray, shape (…, n, n)

Matrices in SPD/HPD manifold.

Notes

Added in version 0.8.

References

[1]

Wasserstein Riemannian geometry of Gaussian densities L. Malagò, L. Montrucchio, G. Pistone. Information Geometry, 2018, 1, pp. 137–179.