Graded persistence diagrams and persistence landscapes

DOI10.1007/s00454-021-00316-1OpenAlexW3185924222MaRDI QIDQ2066309

Peter Bubenik, Leo Betthauser, Parker B. Edwards

Publication date: 14 January 2022

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.12807

zbMATH Keywords

stabilityMöbius inversionrank functionWasserstein distancepersistence modulepersistent homologygraded rank function

Mathematics Subject Classification ID

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

Related Items (4)

Edit Distance and Persistence Diagrams over Lattices ⋮ Homological approximations in persistence theory ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces

Uses Software

• Persistence Landscape

Cites Work

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• A persistence landscapes toolbox for topological statistics
• Stability of persistence diagrams
• Metrics for generalized persistence modules
• Generalized persistence diagrams
• Computing persistent homology
• Erosion distance for generalized persistence modules
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• Multiparameter Persistence Landscapes
• Bottleneck stability for generalized persistence diagrams
• The Persistence Landscape and Some of Its Properties
• Statistical topological data analysis using persistence landscapes
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]

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