Efficient Computation of Image Persistence
Uložené v:
| Názov: | Efficient Computation of Image Persistence |
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| Autori: | Bauer, Ulrich, Schmahl, Maximilian |
| Prispievatelia: | Ulrich Bauer and Maximilian Schmahl |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | arXiv, 2022. |
| Rok vydania: | 2022 |
| Predmety: | Computational Geometry (cs.CG), FOS: Computer and information sciences, 0102 computer and information sciences, 01 natural sciences, image persistence, FOS: Mathematics, Computer Science - Computational Geometry, Algebraic Topology (math.AT), Persistent homology, Mathematics - Algebraic Topology, ddc:004, 0101 mathematics, barcode computation |
| Popis: | We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These algorithms make use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. They form the basis for our implementation for Vietoris-Rips complexes in the framework of the software Ripser. 16 pages |
| Druh dokumentu: | Article Conference object |
| Popis súboru: | application/pdf |
| DOI: | 10.48550/arxiv.2201.04170 |
| DOI: | 10.4230/lipics.socg.2023.14 |
| Prístupová URL adresa: | http://arxiv.org/abs/2201.04170 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.14 |
| Rights: | arXiv Non-Exclusive Distribution CC BY |
| Prístupové číslo: | edsair.doi.dedup.....7a1c9d3b9151e52ddf6b0d8df50e4c6a |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These algorithms make use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. They form the basis for our implementation for Vietoris-Rips complexes in the framework of the software Ripser.<br />16 pages |
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| DOI: | 10.48550/arxiv.2201.04170 |