Exploring uses of persistent homology for statistical analysis of landmark-based shape data

DOI10.1016/j.jmva.2010.04.016zbMath1203.62116OpenAlexW2000375636MaRDI QIDQ990901

Jennifer Gamble, Giseon Heo

Publication date: 1 September 2010

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2010.04.016

zbMATH Keywords

Wasserstein distanceshape analysismultidimensional scalingpersistent homologylandmark-based datapersistence diagrams

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Multivariate analysis (62H99) Applications of statistics to biology and medical sciences; meta analysis (62P10) Simplicial sets and complexes in algebraic topology (55U10)

Related Items (10)

Topological data analysis of single-trial electroencephalographic signals ⋮ Geometry Helps to Compare Persistence Diagrams ⋮ The persistent homology of a self-map ⋮ On the topological data analysis extensions and comparisons ⋮ Statistical Analysis of Locally Parameterized Shapes ⋮ Persistent homology transform for modeling shapes and surfaces ⋮ Persistent homology of graph-like digital images ⋮ Hypothesis testing for topological data analysis ⋮ A persistence landscapes toolbox for topological statistics ⋮ Probabilistic Fréchet means for time varying persistence diagrams

Uses Software

• LFM-Pro

Cites Work

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• Lipschitz functions have \(L_{p}\)-stable persistence
• Matching theory
• Computing persistent homology
• Topological persistence and simplification
• A statistical approach to persistent homology
• Modern multidimensional scaling. Theory and applications.
• An Invariant Approach to Statistical Analysis of Shapes
• Statistical topology via Morse theory, persistence and nonparametric estimation
• Topology and data
• Topology for Computing
• Barcodes: The persistent topology of data

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