Efficient computation of image persistence

• Verfasst von: Bauer, Ulrich [VerfasserIn]
• Verfasst von: Schmahl, Maximilian [VerfasserIn]
• Titel: Efficient computation of image persistence
• Verf.angabe: Ulrich Bauer, Maximilian Schmahl
• E-Jahr: 2022
• Jahr: January 13, 2022
• Umfang: 16 S.
• Fussnoten: Version 1 vom 11 Januar 2022 ; Gesehen am 13.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2022
• Band/Heft Quelle: (2022), Artikel-ID 2201.04170, Seite 1-16
• DOI: doi:10.48550/arXiv.2201.04170
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Computer Science - Computational Geometry
• Sach-SW: Mathematics - Algebraic Topology
• K10plus-PPN: 1818870568

Abstract

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.