Generalized persistence diagrams

DOI10.1007/s41468-018-0012-6zbMath1398.18015arXiv1601.03107OpenAlexW2588688245MaRDI QIDQ1616396

R. Smith

Publication date: 6 November 2018

Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.03107

zbMATH Keywords

Möbius inversionabelian categorysymmetric monoidal categorypersistence diagrams

Mathematics Subject Classification ID

Abelian categories, Grothendieck categories (18E10)

Related Items (23)

The Persistent Homology of Cyclic Graphs ⋮ Capturing dynamics of time-varying data via topology ⋮ Edit Distance and Persistence Diagrams over Lattices ⋮ Universality of the homotopy interleaving distance ⋮ Steady and ranging sets in graph persistence ⋮ Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications ⋮ Bottleneck stability for generalized persistence diagrams ⋮ Exact weights, path metrics, and algebraic Wasserstein distances ⋮ Homological approximations in persistence theory ⋮ On the Stability of Multigraded Betti Numbers and Hilbert Functions ⋮ Unnamed Item ⋮ Spatiotemporal persistent homology for dynamic metric spaces ⋮ Persistent local systems ⋮ Elder-Rule-Staircodes for Augmented Metric Spaces ⋮ Unnamed Item ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Graded persistence diagrams and persistence landscapes ⋮ Topological spaces of persistence modules and their properties ⋮ The fiber of the persistence map for functions on the interval ⋮ Generalized persistence algorithm for decomposing multiparameter persistence modules ⋮ Decorated merge trees for persistent topology ⋮ Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces ⋮ Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology

Cites Work

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• Categorified Reeb graphs
• Stability of persistence diagrams
• Metrics for generalized persistence modules
• Computing persistent homology
• Topological persistence and simplification
• Notions of Möbius inversion
• Zigzag persistence
• Categorification of persistent homology
• The theory of the interleaving distance on multidimensional persistence modules
• The Structure and Stability of Persistence Modules
• On the Applications of Mobius Inversion in Combinatorial Analysis
• Higher Interpolation and Extension for Persistence Modules
• Proximity of persistence modules and their diagrams
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]

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