pyriemann.utils.distance.distance_kullback¶

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

Kullback-Leibler divergence between SPD/HPD matrices.

The left Kullback-Leibler divergence between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is [1]:

\[d(\mathbf{A},\mathbf{B}) = \frac{1}{2} \left( \text{tr}(\mathbf{B}^{-1}\mathbf{A}) - n + \log \left( \frac{\det(\mathbf{B})}{\det(\mathbf{A})}\right) \right)\]

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 (…,): Left Kullback-Leibler divergence between A and B.