Inverse Problems in Topological Persistence

DOI10.1007/978-3-030-43408-3_16zbMath1447.55006arXiv1810.10813OpenAlexW2898403988MaRDI QIDQ5118378

Steve Y. Oudot, Elchanan Solomon

Publication date: 8 September 2020

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

Full work available at URL: https://arxiv.org/abs/1810.10813

zbMATH Keywords

surveybarcodestabilityinversesmachine learningtopological data analysistransformpersistent homologypoint cloudextraction

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Statistical aspects of big data and data science (62R07) Computational aspects of data analysis and big data (68T09)

Related Items (5)

The fiber of persistent homology for simplicial complexes ⋮ From trees to barcodes and back again. II: Combinatorial and probabilistic aspects of a topological inverse problem ⋮ Euler characteristic surfaces ⋮ A statistical pipeline for identifying physical features that differentiate classes of 3D shapes ⋮ Decorated merge trees for persistent topology

Uses Software

• GitHub
• EulerCurves

Cites Work

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• Persistence stability for geometric complexes
• A complete characterization of the one-dimensional intrinsic Čech persistence diagrams for metric graphs
• Continuation of point clouds via persistence diagrams
• Persistent homology and Euler integral transforms
• The theory of the interleaving distance on multidimensional persistence modules
• The Structure and Stability of Persistence Modules
• Topology and data
• Persistent homology transform for modeling shapes and surfaces
• Induced Matchings of Barcodes and the Algebraic Stability of Persistence
• Decomposition of pointwise finite-dimensional persistence modules
• Comparing Graphs via Persistence Distortion
• Stability of persistence diagrams
• Proximity of persistence modules and their diagrams
• Persistence-Based Clustering in Riemannian Manifolds
• Barcodes: The persistent topology of data

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