Elder-Rule-Staircodes for Augmented Metric Spaces

DOI10.1137/20M1353605zbMath1477.55005arXiv2003.04523OpenAlexW3011959994MaRDI QIDQ4959123

Chen Cai, Facundo Mémoli, Yusu Wang, Woojin Kim

Publication date: 10 September 2021

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04523

zbMATH Keywords

hierarchical clusteringpersistence diagrammultiparameter persistent homologyelder-rule

Mathematics Subject Classification ID

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

Related Items (2)

Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications ⋮ Generalized persistence algorithm for decomposing multiparameter persistence modules

Uses Software

• RIVET

Cites Work

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• Combinatorial presentation of multidimensional persistent homology
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• The power of geometric duality
• Algorithms for updating minimal spanning trees
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• Algebraic stability of zigzag persistence modules
• The rank invariant stability via interleavings
• Computing persistent homology
• Topological persistence and simplification
• Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
• Spatiotemporal persistent homology for dynamic metric spaces
• A density-sensitive hierarchical clustering method
• The fiber of the persistence map for functions on the interval
• The theory of the interleaving distance on multidimensional persistence modules
• A refinement of multi-dimensional persistence
• Betti numbers in multidimensional persistent homology are stable functions
• Multiparameter Persistence Landscapes
• Stratifying Multiparameter Persistent Homology
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem

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