Same But Different: Distance Correlations Between Topological Summaries

DOI10.1007/978-3-030-43408-3_18zbMath1450.62141arXiv1903.01051OpenAlexW2920595754MaRDI QIDQ5118380

Katharine Turner, Gard Spreemann

Publication date: 8 September 2020

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

Full work available at URL: https://arxiv.org/abs/1903.01051

zbMATH Keywords

distance correlationstopological summaries

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Persistent homology and applications, topological data analysis (55N31) Topological data analysis (62R40)

Related Items (8)

Persistence curves: a canonical framework for summarizing persistence diagrams ⋮ A new measure for the attitude to mobility of Italian students and graduates: a topological data analysis approach ⋮ Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams ⋮ Embeddings of persistence diagrams into Hilbert spaces ⋮ Describing topology on the set of persistence diagrams ⋮ Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric ⋮ The space of persistence diagrams on $n$ points coarsely embeds into Hilbert space ⋮ Graph pseudometrics from a topological point of view

Uses Software

• Persistence Landscape
• GitHub
• Ripser
• Flagser

Cites Work

• Measuring and testing dependence by correlation of distances
• Hypothesis testing for topological data analysis
• Positive definite metric spaces
• Distance covariance in metric spaces
• A persistence landscapes toolbox for topological statistics
• Fréchet means for distributions of persistence diagrams
• Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
• Cone fields and topological sampling in manifolds with bounded curvature
• Kernel method for persistence diagrams via kernel embedding and weight factor
• Geometry Helps to Compare Persistence Diagrams
• Statistical topological data analysis using persistence landscapes

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