Efficient computation of image persistence
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 homo...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
January 13, 2022
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| In: |
Arxiv
Year: 2022, Pages: 1-16 |
| DOI: | 10.48550/arXiv.2201.04170 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2201.04170 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2201.04170 
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| Verfasserangaben: | Ulrich Bauer, Maximilian Schmahl |
| Zusammenfassung: | 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. |
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| Beschreibung: | Version 1 vom 11 Januar 2022 Gesehen am 13.10.2022 |
| Beschreibung: | Online Resource |
| DOI: | 10.48550/arXiv.2201.04170 |