Decomposing filtered chain complexes: geometry behind barcoding algorithms

DOI10.1016/j.comgeo.2022.101938OpenAlexW4293833413WikidataQ114195418 ScholiaQ114195418MaRDI QIDQ2096381

Alvin Jin, Barbara Giunti, Wojciech Chachólski, Landi, Claudia

Publication date: 16 November 2022

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.01033

zbMATH Keywords

topological data analysisclear and compressfiltered chain complexesfiltered kernelsinterval spherespersistence algorithms

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Chain complexes in algebraic topology (55U15)

Uses Software

• Gudhi
• Dionysus
• Ripser

Cites Work

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• Ripser: efficient computation of Vietoris-Rips persistence barcodes
• Persistent homology and Floer-Novikov theory
• An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere
• \textsc{Phat} -- persistent homology algorithms toolbox
• On the use of size functions for shape analysis
• Computing persistent homology
• Topological persistence and simplification
• Zigzag persistence
• Tri-partitions and bases of an ordered complex
• Invariants for tame parametrised chain complexes
• On the structural theorem of persistent homology
• javaPlex: A Research Software Package for Persistent (Co)Homology
• The Gudhi Library: Simplicial Complexes and Persistent Homology
• Dualities in persistent (co)homology
• On a right inverse mapping of a simplicial mapping
• Clear and Compress: Computing Persistent Homology in Chunks
• Topology and data
• Combinatorial realization of the Thom-Smale complex via discrete Morse theory
• Persistence modules on commutative ladders of finite type

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