Filtration simplification for persistent homology via edge contraction

DOI10.1007/s10851-020-00956-7zbMath1494.55008arXiv1810.04388OpenAlexW2951606678MaRDI QIDQ2203349

Ryan Slechta, Tamal Krishna Dey

Publication date: 6 October 2020

Published in: Journal of Mathematical Imaging and Vision, Discrete Geometry for Computer Imagery (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04388

zbMATH Keywords

topological data analysispersistent homologyedge contraction

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31)

Related Items (2)

Filtration simplification for persistent homology via edge contraction ⋮ Computing Persistent Homology of Flag Complexes via Strong Collapses

Uses Software

• GitHub
• SimBa
• Sophia

Cites Work

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• Strong homotopy types, nerves and collapses
• Graph minors. XX: Wagner's conjecture
• The theory of multidimensional persistence
• Graph minors. I. Excluding a forest
• Topological persistence and simplification
• Filtration simplification for persistent homology via edge contraction
• The theory of the interleaving distance on multidimensional persistence modules
• The Structure and Stability of Persistence Modules
• Geometry Helps to Compare Persistence Diagrams
• Barcodes of Towers and a Streaming Algorithm for Persistent Homology
• SimBa: An Efficient Tool for Approximating Rips-filtration Persistence via Simplicial Batch-collapse
• Computing Topological Persistence for Simplicial Maps
• Strong Collapse for Persistence
• Stability of persistence diagrams
• Proximity of persistence modules and their diagrams

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