aspcol.distance.covariance_distance_riemannian

aspcol.distance.covariance_distance_riemannian(mat1, mat2)

Computes the covariance matrix distance

Parameters:

  • mat1 (np.ndarray of shape (N, N)) – First covariance matrix, should be symmetric and positive definite

  • mat2 (np.ndarray of shape (N, N)) – Second covariance matrix, should be symmetric and positive definite

Returns:

dist – The distance between the two matrices

Return type:

float

Notes

It is the distance of a canonical invariant Riemannian metric on the space Sym+(n, R) of real symmetric positive definite matrices.

Invariant to affine transformations and inversions. It is a distance measure, so 0 means equal and then it goes to infinity and the matrices become more unequal.

When the metric of the space is the fisher information metric, this is the distance of the space. See COVARIANCE CLUSTERING ON RIEMANNIAN MANIFOLDS FOR ACOUSTIC MODEL COMPRESSION - Shinohara, Masukp, Akamine

References

[forstnermetric2003] [absilOptimization2008]