Topological and metric properties of spaces of generalized persistence diagrams

DOI10.1007/S41468-023-00157-2MaRDI QIDQ6589172

Iryna Hartsock, Peter Bubenik

Publication date: 19 August 2024

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

zbMATH Keywords

Wasserstein distancetopological data analysispersistent homologyformal sums on metric spaces

Mathematics Subject Classification ID

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Cites Work

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• Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
• Fréchet means for distributions of persistence diagrams
• Stability of persistence diagrams
• Asymptotic dimension
• Lipschitz functions have \(L_{p}\)-stable persistence
• Countability properties of function spaces
• Algebraic stability of zigzag persistence modules
• Numeric invariants from multidimensional persistence
• On the stability of interval decomposable persistence modules
• Generalized persistence diagrams for persistence modules over posets
• Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces
• Universality of persistence diagrams and the bottleneck and Wasserstein distances
• Embeddings of persistence diagrams into Hilbert spaces
• Medians of populations of persistence diagrams
• Decomposition of exact pfd persistence bimodules
• Topological spaces of persistence modules and their properties
• A course in metric geometry
• The asymptotic dimension of quotients by finite groups
• Probability measures on the space of persistence diagrams
• Support Vector Machines
• A.D. Alexandrov spaces with curvature bounded below
• Topological Data Analysis for Genomics and Evolution
• Barycenters in Alexandrov spaces of curvature bounded below
• Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
• The space of persistence diagrams on $n$ points coarsely embeds into Hilbert space
• Computational Topology for Data Analysis
• Topological Data Analysis with Applications
• Approximating continuous functions on persistence diagrams using template functions
• Persistence Over Posets

Related Items (1)

Metric geometry of spaces of persistence diagrams

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