Efficient and robust persistent homology for measures

DOI10.1016/j.comgeo.2016.07.001zbMath1357.65022arXiv1306.0039OpenAlexW2201541687MaRDI QIDQ340536

Mickaël Buchet, Steve Y. Oudot, Donald R. Sheehy, Fréderic Chazal

Publication date: 14 November 2016

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0039

zbMATH Keywords

topological data analysispersistent homologydistance to a measuresparse rips filtration

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items

Geometric Approaches to Persistent Homology ⋮ A Topological Data Analysis Approach on Predicting Phenotypes from Gene Expression Data ⋮ Rates of convergence for robust geometric inference ⋮ A limit theorem for persistence diagrams of random filtered complexes built over marked point processes ⋮ Recovering the homology of immersed manifolds ⋮ DTM-Based Filtrations ⋮ Persistent homology for low-complexity models ⋮ Unnamed Item ⋮ Weighted persistent homology ⋮ Computational tools in weighted persistent homology ⋮ Unnamed Item ⋮ Dimensionality reduction for \(k\)-distance applied to persistent homology ⋮ Sparse Dowker nerves ⋮ A comparison framework for interleaved persistence modules ⋮ Compression for \(2\)-parameter persistent homology

Uses Software

• CGAL
• ANN
• 3D Alpha Shapes

Cites Work

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• Persistence stability for geometric complexes
• Geometric inference for probability measures
• Stability of persistence diagrams
• A sampling theory for compact sets in Euclidean space
• Computing persistent homology
• Applications of random sampling in computational geometry. II
• Topological persistence and simplification
• Witnessed \(k\)-distance
• Linear-size approximations to the Vietoris-Rips filtration
• Finding the homology of submanifolds with high confidence from random samples
• The Structure and Stability of Persistence Modules
• Towards persistence-based reconstruction in euclidean spaces
• Topology and data
• Computing Topological Persistence for Simplicial Maps
• Zigzag zoology
• Proximity of persistence modules and their diagrams

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