Geometric statistics with subspace structure preservation for SPD matrices

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Mostajeran, Cyrus, Nathaël Da Costa, Graham Van Goffrier, Sepulchre, Rodolphe
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.07.2024
Subjects
Eigenvalues
Matrices (mathematics)
Subspaces
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Summary: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.
ISSN:2331-8422