Geometric statistics with subspace structure preservation for SPD matrices

Autor:	Mostajeran, Cyrus, Da Costa, Nathaël, Van Goffrier, Graham, Sepulchre, Rodolphe
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning Mathematics - Differential Geometry Statistics - Computation
Druh dokumentu:	Working Paper
Popis:	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. Comment: arXiv admin note: substantial text overlap with arXiv:2304.07347
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.03382 Zobrazit plný text záznamu View this record from Arxiv