spd_learn.functional.mean_riemann#

spd_learn.functional.mean_riemann(X, *, tol=1e-08, maxiter=50, init=None, sample_weight=None)[source]#

Mean of SPD/HPD matrices according to the Riemannian metric.

The affine-invariant Riemannian mean minimizes the sum of squared affine-invariant Riemannian distances \(d_R\) to all SPD/HPD matrices [1]:

\[\arg \min_{\mathbf{M}} \sum_i w_i \ d_R (\mathbf{M}, \mathbf{X}_i)^2\]

with \(w\) being the weights which sum to 1.

For the convergence, the implemented stopping criterion comes from [2].

Parameters:

X (ndarray, shape (..., n_matrices, n, n)) – Set of SPD/HPD matrices.
tol (float, default=10e-9) – Tolerance to stop the gradient descent.
maxiter (int, default=50) – Maximum number of iterations.
init (None | 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_weight (None | ndarray, shape (n_matrices,), default=None) – Weights for each matrix. If None, it uses equal weights.

Returns:

M – Affine-invariant Riemannian mean.

Return type:

ndarray, shape (…, n, n)

Notes

Changed in version 0.12: Add support for NumPy and PyTorch.