Geometric statistics with subspace structure preservation for SPD matrices

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Mostajeran, Cyrus, Da Costa, Nathaël, Van Goffrier, Graham, Sepulchre, Rodolphe
Format: Preprint
Veröffentlicht: 2024
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866914857799909376
author Mostajeran, Cyrus
Da Costa, Nathaël
Van Goffrier, Graham
Sepulchre, Rodolphe
author_facet Mostajeran, Cyrus
Da Costa, Nathaël
Van Goffrier, Graham
Sepulchre, Rodolphe
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_03382
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Geometric statistics with subspace structure preservation for SPD matrices
Mostajeran, Cyrus
Da Costa, Nathaël
Van Goffrier, Graham
Sepulchre, Rodolphe
Numerical Analysis
Machine Learning
Differential Geometry
Computation
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.
title Geometric statistics with subspace structure preservation for SPD matrices
topic Numerical Analysis
Machine Learning
Differential Geometry
Computation
url https://arxiv.org/abs/2407.03382