Certified Mapper: Repeated Testing for Acyclicity and Obstructions to the Nerve Lemma

DOI10.1007/978-3-030-43408-3_19zbMath1450.62142arXiv1808.09933OpenAlexW2888854805MaRDI QIDQ5118382

Alisa Leshchenko, Mikael Vejdemo-Johansson

Publication date: 8 September 2020

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

Full work available at URL: https://arxiv.org/abs/1808.09933

zbMATH Keywords

acyclicitynerve lemmarepeated testing

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Paired and multiple comparisons; multiple testing (62J15) Topological data analysis (62R40)

Related Items (2)

Intrinsic disease maps using persistent cohomology ⋮ Multiple hypothesis testing with persistent homology

Uses Software

• spatial
• TDAmapper
• bootlib

Cites Work

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• Confidence sets for persistence diagrams
• bootlib
• Symmetric and \(r\)-symmetric tropical polynomials and rational functions
• The ring of algebraic functions on persistence bar codes
• Structure and stability of the one-dimensional Mapper
• Maximally persistent cycles in random geometric complexes
• An approximate nerve theorem
• Crackle: the homology of noise
• Convergence between Categorical Representations of Reeb Space and Mapper
• Theoretical Statistics
• Topology and data
• A sharper Bonferroni procedure for multiple tests of significance
• Statistical Analysis and Parameter Selection for Mapper
• Multiscale Mapper: Topological Summarization via Codomain Covers
• The Morse Theory of Čech and Delaunay Filtrations

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