Bipath Persistence
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916191108333568 |
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| author | Aoki, Toshitaka Escolar, Emerson G. Tada, Shunsuke |
| author_facet | Aoki, Toshitaka Escolar, Emerson G. Tada, Shunsuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bipath Persistence Aoki, Toshitaka Escolar, Emerson G. Tada, Shunsuke Algebraic Topology Representation Theory 55N31, 68W30, 16G20, 16Z05 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. |
| title | Bipath Persistence |
| topic | Algebraic Topology Representation Theory 55N31, 68W30, 16G20, 16Z05 |
| url | https://arxiv.org/abs/2404.02536 |