pyriemann.utils.mean.mean_logdet

pyriemann.utils.mean.mean_logdet(X, *, tol=0.0001, maxiter=50, init=None, sample_weight=None)

Mean of SPD/HPD matrices according to the log-det metric.

Log-det mean is obtained by an iterative procedure where the update is:

\[\mathbf{M} = \left( \sum_i w_i \ \left( 0.5 \mathbf{M} + 0.5 \mathbf{X}_i \right)^{-1} \right)^{-1}\]

Parameters:

Xndarray, shape (n_matrices, n, n)

Set of SPD/HPD matrices.

tolfloat, default=10e-5

Tolerance to stop the gradient descent.

maxiterint, default=50

Maximum number of iterations.

initNone | ndarray, shape (n, n), default=None

A SPD/HPD matrix used to initialize the gradient descent. If None, the weighted Euclidean mean is used.

sample_weightNone | ndarray, shape (n_matrices,), default=None

Weights for each matrix. If None, it uses equal weights.

Returns:

Mndarray, shape (n, n)

Log-det mean.

See also

mean_covariance