Approximating persistent homology in Euclidean space through collapses

DOI10.1007/s00200-014-0247-yzbMath1320.55002arXiv1403.0533OpenAlexW2063954846MaRDI QIDQ2352514

Magnus Bakke Botnan, Gard Spreemann

Publication date: 2 July 2015

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0533

zbMATH Keywords

approximationpersistent homologycomputational topologybottleneck distance

Mathematics Subject Classification ID

Theory of data (68P99) ?ech types (55N05)

Related Items (15)

Strong collapse and persistent homology ⋮ The Offset Filtration of Convex Objects ⋮ The Persistent Homology of Cyclic Graphs ⋮ Barcodes of towers and a streaming algorithm for persistent homology ⋮ Universality of the homotopy interleaving distance ⋮ A unified view on the functorial nerve theorem and its variations ⋮ Quantitative simplification of filtered simplicial complexes ⋮ Polynomial-sized topological approximations using the permutahedron ⋮ Strong Collapse for Persistence ⋮ Improved approximate Rips filtrations with shifted integer lattices and cubical complexes ⋮ Improved Approximate Rips Filtrations with Shifted Integer Lattices ⋮ An approximate nerve theorem ⋮ Computing Persistent Homology of Flag Complexes via Strong Collapses ⋮ A comparison framework for interleaved persistence modules ⋮ Compression for \(2\)-parameter persistent homology

Uses Software

• Miniball
• fastcluster

Cites Work

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