Signal classification with a point process distance on the space of persistence diagrams

DOI10.1007/s11634-017-0294-xzbMath1416.94030OpenAlexW2761524068MaRDI QIDQ1630882

Andrew Marchese, Vasileios Maroulas

Publication date: 5 December 2018

Published in: Advances in Data Analysis and Classification. ADAC (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11634-017-0294-x

zbMATH Keywords

Wasserstein metriccardinalitypersistent homologyclassification of time seriesdata space of persistence diagrams

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Other homology theories in algebraic topology (55N35)

Related Items (9)

Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams ⋮ Bayesian topological signal processing ⋮ Bayesian topological learning for classifying the structure of biological networks ⋮ Topological learning for brain networks ⋮ ToFU: topology functional units for deep learning ⋮ A stable cardinality distance for topological classification ⋮ Geometric Metrics for Topological Representations ⋮ A random persistence diagram generator ⋮ A Bayesian Framework for Persistent Homology

Uses Software

• Dionysus
• TDA
• GitHub
• Ripser

Cites Work

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• The ring of algebraic functions on persistence bar codes
• Fréchet means for distributions of persistence diagrams
• Tracking rapid intracellular movements: a Bayesian random set approach
• Lipschitz functions have \(L_{p}\)-stable persistence
• Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
• Crackle: the homology of noise
• Probability measures on the space of persistence diagrams
• Topology and data
• A Consistent Metric for Performance Evaluation of Multi-Object Filters
• Geometry Helps to Compare Persistence Diagrams
• Data Assimilation
• Proximity of persistence modules and their diagrams
• Statistical topological data analysis using persistence landscapes

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