pyriemann.utils.distance.distance_riemann

pyriemann.utils.distance.distance_riemann(A, B, squared=False)

Affine-invariant Riemannian distance between SPD/HPD matrices.

The affine-invariant Riemannian distance between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is [1]:

\[d(\mathbf{A},\mathbf{B}) = \Vert \log(\mathbf{B}^{-1/2} \mathbf{A} \mathbf{B}^{-1/2}) \Vert_F = {\left( \sum_i \log(\lambda_i)^2 \right)}^{1/2}\]

where \(\lambda_i\) are the joint eigenvalues of \(\mathbf{A}\) and \(\mathbf{B}\).

Parameters:

Andarray, shape (…, n, n)

First SPD/HPD matrices, at least 2D ndarray.

Bndarray, shape (…, n, n)

Second SPD/HPD matrices, same dimensions as A.

squaredbool, default=False

Return squared distance.

Added in version 0.5.

Returns:

dfloat or ndarray, shape (…,)

Affine-invariant Riemannian distance between A and B.

See also

distance

References

[1]

A metric for covariance matrices W. Förstner & B. Moonen. Geodesy-the Challenge of the 3rd Millennium, 2003