Fast computation of persistent homology representatives with involuted persistent homology
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929587781369856 |
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| author | Čufar, Matija Virk, Žiga |
| author_facet | Čufar, Matija Virk, Žiga |
| contents | Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of homology representatives. The mentioned representatives are geometric manifestations of the corresponding holes and often carry desirable information.
We propose a new method of extraction of persistent homology representatives using cohomology. In a nutshell, we first compute persistent cohomology and use the obtained information to significantly improve the running time of the direct persistent homology computations. This algorithm applied to Rips filtrations generally computes persistent homology representatives much faster than the standard methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_03629 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fast computation of persistent homology representatives with involuted persistent homology Čufar, Matija Virk, Žiga Algebraic Topology Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of homology representatives. The mentioned representatives are geometric manifestations of the corresponding holes and often carry desirable information. We propose a new method of extraction of persistent homology representatives using cohomology. In a nutshell, we first compute persistent cohomology and use the obtained information to significantly improve the running time of the direct persistent homology computations. This algorithm applied to Rips filtrations generally computes persistent homology representatives much faster than the standard methods. |
| title | Fast computation of persistent homology representatives with involuted persistent homology |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2105.03629 |