spd_learn.functional.mean_ale#

spd_learn.functional.mean_ale(X, *, tol=1e-06, maxiter=50, sample_weight=None, init=None)[source]#

AJD-based log-Euclidean (ALE) mean of SPD/HPD matrices.

Approximate joint diagonalization (AJD) based log-Euclidean (ALE) mean of SPD/HPD matrices [1].

Parameters:

  • X (ndarray, shape (..., n_matrices, n, n)) – Set of SPD/HPD matrices.

  • tol (float, default=10e-7) – Tolerance to stop the gradient descent.

  • maxiter (int, default=50) – Maximum number of iterations.

  • sample_weight (None | ndarray, shape (n_matrices,), default=None) – Weights for each matrix. If None, it uses equal weights.

  • init (None | ndarray, shape (n, n), default=None) – A SPD/HPD matrix used to initialize the gradient descent. If None, the joint diagonalizer of input matrices is used.

Returns:

M – ALE mean.

Return type:

ndarray, shape (…, n, n)

Notes

Added in version 0.2.4.

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

See also

gmean

References

[1]

Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices M. Congedo, B. Afsari, A. Barachant, M. Moakher. PLOS ONE, 2015