Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem

DOI10.1007/978-3-030-43408-3_3zbMath1453.55004arXiv1610.10085OpenAlexW2546347714MaRDI QIDQ5118359

Ulrich Bauer, Michael Lesnick

Publication date: 8 September 2020

Published in: Topological Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.10085

zbMATH Keywords

categorical structurestability theoremmatching theorem

Mathematics Subject Classification ID

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

Related Items

Persistent extensions and analogous bars: data-induced relations between persistence barcodes, Partial matchings induced by morphisms between persistence modules, Persistent homology and microlocal sheaf theory, Topological spaces of persistence modules and their properties, A comparison framework for interleaved persistence modules, Decorated merge trees for persistent topology

Cites Work

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• Confidence sets for persistence diagrams
• Categorified Reeb graphs
• Stability of persistence diagrams
• The persistent homology of a self-map
• Metrics for generalized persistence modules
• Korrespondenzen in abelschen Kategorien
• Algebraic stability of zigzag persistence modules
• Categorification of persistent homology
• The theory of the interleaving distance on multidimensional persistence modules
• Linear-size approximations to the Vietoris-Rips filtration
• Induced Matchings and the Algebraic Stability of Persistence Barcodes
• Homological Algebra
• The Structure and Stability of Persistence Modules
• Decomposition of pointwise finite-dimensional persistence modules
• Visualizing Sparse Filtrations.
• Proximity of persistence modules and their diagrams