pyriemann.utils.distance.distance_kullback

pyriemann.utils.distance.distance_kullback(A, B)

Kullback-Leibler divergence between SPD matrices.

The left Kullback-Leibler divergence between two SPD matrices A and B is:

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

Parameters

Andarray, shape (…, n, n)

First SPD matrices, at least 2D ndarray.

Bndarray, shape (…, n, n)

Second SPD matrices, same dimensions as A.

Returns

dndarray, shape (…,) or float

Left Kullback-Leibler divergence between A and B.