spd_learn.functional.exp_map_wasserstein#

spd_learn.functional.exp_map_wasserstein(X, Cref, **kwargs)[source]#

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:

  • X (ndarray, shape (..., n, n)) – Matrices in tangent space.

  • Cref (ndarray, shape (n, n)) – Reference SPD/HPD matrix.

Returns:

X_original – Matrices in SPD/HPD manifold.

Return type:

ndarray, shape (…, n, n)

Notes

Added in version 0.8.

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

References

[1]

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