Bipath Persistence
Algebraic Topology
2024-04-04 v1 Representation Theory
Abstract
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology, which can be used to study the persistence of topological features across a pair of filtrations connected at their ends, to compare the two filtrations. In this setting, interval-decomposability is guaranteed, and we provide an algorithm for computing persistence diagrams for bipath persistent homology and discuss the interpretation of bipath persistence diagrams.
Cite
@article{arxiv.2404.02536,
title = {Bipath Persistence},
author = {Toshitaka Aoki and Emerson G. Escolar and Shunsuke Tada},
journal= {arXiv preprint arXiv:2404.02536},
year = {2024}
}
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22 pages