Inductive geometric matrix midranges
Inductive geometric matrix midranges
Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange"centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.
Classification, Clustering, Covariance matrices, Differential geometry
584-589
Van Goffrier, Graham W.
18877be8-d9be-4c90-a625-8f1c11b9cb84
Mostajeran, Cyrus
7b47a1d5-00df-4575-8828-1e473d58f82d
Sepulchre, Rodolphe
84b23c9e-f6b9-4145-873e-55c9ac4b42af
Van Goffrier, Graham W.
18877be8-d9be-4c90-a625-8f1c11b9cb84
Mostajeran, Cyrus
7b47a1d5-00df-4575-8828-1e473d58f82d
Sepulchre, Rodolphe
84b23c9e-f6b9-4145-873e-55c9ac4b42af
Van Goffrier, Graham W., Mostajeran, Cyrus and Sepulchre, Rodolphe
(2021)
Inductive geometric matrix midranges.
IFAC-PapersOnLine, 54 (9), .
(doi:10.1016/j.ifacol.2021.06.120).
Abstract
Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange"centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.
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e-pub ahead of print date: 16 July 2021
Venue - Dates:
24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020, , Cambridge, United Kingdom, 2021-08-23 - 2021-08-27
Keywords:
Classification, Clustering, Covariance matrices, Differential geometry
Identifiers
Local EPrints ID: 482088
URI: http://eprints.soton.ac.uk/id/eprint/482088
ISSN: 2405-8963
PURE UUID: dcb958a3-6404-46f8-83da-c1e6df71b9aa
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Date deposited: 19 Sep 2023 16:33
Last modified: 18 Mar 2024 04:16
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Contributors
Author:
Graham W. Van Goffrier
Author:
Cyrus Mostajeran
Author:
Rodolphe Sepulchre
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