Stratifying Multiparameter Persistent Homology

DOI10.1137/18M1224350zbMath1450.55002arXiv1708.07390WikidataQ115036614 ScholiaQ115036614MaRDI QIDQ5234534

Ulrike Tillmann, Nina Otter, Henry K. Schenck, Heather A. Harrington

Publication date: 27 September 2019

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

Full work available at URL: https://arxiv.org/abs/1708.07390

zbMATH Keywords

Hilbert seriestopological data analysisprimary decompositionpersistent homology

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Simplicial sets and complexes in algebraic topology (55U10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (14)

Multiparameter Persistence Landscapes ⋮ What Are Higher-Order Networks? ⋮ Euler characteristic surfaces ⋮ Computing the multicover bifiltration ⋮ Exact weights, path metrics, and algebraic Wasserstein distances ⋮ Persistence and the Sheaf-Function Correspondence ⋮ On the Stability of Multigraded Betti Numbers and Hilbert Functions ⋮ Computing invariants for multipersistence via spectral systems and effective homology ⋮ A computational framework for connection matrix theory ⋮ Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension ⋮ Elder-Rule-Staircodes for Augmented Metric Spaces ⋮ Homological algebra for persistence modules ⋮ Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology ⋮ Algebraic homotopy interleaving distance

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