Embeddings of persistence diagrams into Hilbert spaces

DOI10.1007/s41468-020-00056-wzbMath1455.55006arXiv1905.05604OpenAlexW2945456722MaRDI QIDQ2209745

Yanyan Li

Publication date: 4 November 2020

Published in: Journal of Applied and Computational Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05604

zbMATH Keywords

coarse geometrykernel methodspersistent homologybottleneck distance

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Lipschitz and coarse geometry of metric spaces (51F30)

Related Items (7)

Persistence curves: a canonical framework for summarizing persistence diagrams ⋮ Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams ⋮ Describing topology on the set of persistence diagrams ⋮ The space of persistence diagrams fails to have Yu's property A ⋮ Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric ⋮ The space of persistence diagrams on $n$ points coarsely embeds into Hilbert space ⋮ Supervised learning with indefinite topological Kernels

Cites Work

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• On a problem of Smirnov
• Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert
• Probability measures on the space of persistence diagrams
• Support Vector Machines
• Uniform Embeddings into Hilbert Space and a Question of Gromov
• Same But Different: Distance Correlations Between Topological Summaries
• Proximity of persistence modules and their diagrams
• Metric Spaces and Positive Definite Functions

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