Computing Representatives of Persistent Homology Generators with a Double Twist
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914706979028992 |
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| author | Pham, Tuyen Wagner, Hubert |
| author_facet | Pham, Tuyen Wagner, Hubert |
| contents | With the growing availability of efficient tools, persistent homology is becoming a useful methodology in a variety of applications. Significant work has been devoted to implementing tools for persistent homology diagrams; however, computing representative cycles corresponding to each point in the diagram can still be inefficient. To circumvent this problem, we extend the twist algorithm of Chen and Kerber. Our extension is based on a new technique we call saving, which supplements their existing killing technique. The resulting two-pass strategy can be realized using an existing matrix reduction implementation as a black-box and improves the efficiency of computing representatives of persistent homology generators. We prove the correctness of the new approach and experimentally show its performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing Representatives of Persistent Homology Generators with a Double Twist Pham, Tuyen Wagner, Hubert Algebraic Topology Computational Geometry With the growing availability of efficient tools, persistent homology is becoming a useful methodology in a variety of applications. Significant work has been devoted to implementing tools for persistent homology diagrams; however, computing representative cycles corresponding to each point in the diagram can still be inefficient. To circumvent this problem, we extend the twist algorithm of Chen and Kerber. Our extension is based on a new technique we call saving, which supplements their existing killing technique. The resulting two-pass strategy can be realized using an existing matrix reduction implementation as a black-box and improves the efficiency of computing representatives of persistent homology generators. We prove the correctness of the new approach and experimentally show its performance. |
| title | Computing Representatives of Persistent Homology Generators with a Double Twist |
| topic | Algebraic Topology Computational Geometry |
| url | https://arxiv.org/abs/2403.04100 |