pyriemann.utils.distance.distance_logeuclid

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

Log-Euclidean distance between SPD/HPD matrices.

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

\[d(\mathbf{A},\mathbf{B}) = \Vert \log(\mathbf{A}) - \log(\mathbf{B}) \Vert_F\]

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 (…,)

Log-Euclidean distance between A and B.

See also

distance

References

[1]

Geometric means in a novel vector space structure on symmetric positive-definite matrices V. Arsigny, P. Fillard, X. Pennec, N. Ayache. SIAM J Matrix Anal Appl, 2007, 29 (1), pp. 328-347