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Proceedings Paper

K−means clustering on the space of persistence diagrams
Author(s): Andrew Marchese; Vasileios Maroulas; Josh Mike
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Paper Abstract

A recent cohort of research aims to apply topological and geometric theory to data analysis. However, more effort is needed to incorporate statistical ideas and structure to these analysis methods. To this end, we present persistent homology clustering techniques through the perspective of data analysis. These techniques provide insight into the structure of the underlying dynamic and are able to recognize important shape properties such as periodicity, chaos, and multi-stability. Moreover, introducing quantitative structure on the topological data space allows for rigorous understanding of the data's geometry, a powerful tool for scrutinizing the morphology of the inherent dynamic. Additionally, we illustrate the advantages of these techniques and results through examples derived from dynamical systems applications.

Paper Details

Date Published: 24 August 2017
PDF: 10 pages
Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940W (24 August 2017); doi: 10.1117/12.2273067
Show Author Affiliations
Andrew Marchese, The Univ. of Tennessee, Knoxville (United States)
Vasileios Maroulas, The Univ. of Tennessee, Knoxville (United States)
Josh Mike, The Univ. of Tennessee, Knoxville (United States)

Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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