Geometric statistics with subspace structure preservation for SPD matrices
Numerical Analysis
2024-07-08 v1 Machine Learning
Numerical Analysis
Differential Geometry
Computation
Abstract
We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalues. This is achieved through the use of the Thompson geometry of the semidefinite cone. We explore a particular geodesic space structure in detail and establish several properties associated with it. Finally, we review a novel inductive mean of SPD matrices based on this geometry.
Keywords
Cite
@article{arxiv.2407.03382,
title = {Geometric statistics with subspace structure preservation for SPD matrices},
author = {Cyrus Mostajeran and Nathaël Da Costa and Graham Van Goffrier and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:2407.03382},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2304.07347