Fast topological signal identification and persistent cohomological cycle matching
File(s)
Published version
Author(s)
García-Redondo, Inés
Monod, Anthea
Song, Anna
Type
Journal Article
Abstract
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions to these problems, however, is computational speed. In this paper, we harness the state-of-the-art for persistent homology computation by studying the problem of determining topological prevalence and cycle matching using a cohomological approach, which increases their feasibility and applicability to a wider variety of applications and contexts. We demonstrate this approach on a wide range of real-life, large-scale, and complex datasets. We extend existing notions of topological prevalence and cycle matching to include general non-Morse filtrations. This provides the most general and flexible state-of-the-art adaptation of topological signal identification and persistent cycle matching, which performs comparisons of orders of ten for thousands of sampled points in a matter of minutes on standard institutional HPC CPU facilities.
Date Issued
2024-09-01
Date Acceptance
2024-05-31
Citation
Journal of Applied and Computational Topology, 2024, 8 (3), pp.695-726
ISSN
2367-1726
Publisher
Springer
Start Page
695
End Page
726
Journal / Book Title
Journal of Applied and Computational Topology
Volume
8
Issue
3
Copyright Statement
© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Publication Status
Published
Date Publish Online
2024-06-24