Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre
{"title":"Geometric statistics with subspace structure preservation for SPD matrices","authors":"Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre","doi":"arxiv-2407.03382","DOIUrl":null,"url":null,"abstract":"We present a geometric framework for the processing of SPD-valued data that\npreserves subspace structures and is based on the efficient computation of\nextreme generalized eigenvalues. This is achieved through the use of the\nThompson geometry of the semidefinite cone. We explore a particular geodesic\nspace structure in detail and establish several properties associated with it.\nFinally, we review a novel inductive mean of SPD matrices based on this\ngeometry.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.03382","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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