Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values

The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. I...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Bapat, Asilata, Brooks, Robyn, Hacker, Celia, Landi, Claudia, Mahler, Barbara I, Stephenson, Elizabeth R
Format: Article
Language:English
Subjects:
Computation
Data analysis
Homology
Matching
Modules
Parameters
Topology
Online Access:Get full text
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Summary:The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.
ISSN:2331-8422