Goffrier, GWV;
Mostajeran, C;
Sepulchre, R;
(2021)
Inductive Geometric Matrix Midranges.
In: Sepulchre, R, (ed.)
Proceedings of the 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020.
(pp. pp. 584-589).
Elsevier: Cambridge, UK.
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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.
| Type: | Proceedings paper |
|---|---|
| Title: | Inductive Geometric Matrix Midranges |
| Event: | 24th InternationalSymposium on Mathematical Theory of Networks and Systems MTNS 2020 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.ifacol.2021.06.120 |
| Publisher version: | http://dx.doi.org/10.1016/j.ifacol.2021.06.120 |
| Language: | English |
| Additional information: | Copyright © The Authors 2021. This is an Open Access article published under a Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Classification, Clustering, Covariance Matrices, Differential Geometry |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10139534 |
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