Probabilistic Fréchet means for time varying persistence diagrams

DOI10.1214/15-EJS1030zbMath1348.68285arXiv1307.6530OpenAlexW1819250359MaRDI QIDQ2346527

Elizabeth Munch, Paul Bendich, Katharine Turner, Sayan Mukherjee, Jonathan C. Mattingly, John L. Harer

Publication date: 2 June 2015

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.6530

zbMATH Keywords

variancepersistent homologyFréchet meanpersistence diagramtime-varying datatopological data analysis (TDA)vineyard

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Probability measures on topological spaces (60B05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)

Related Items

Persistence landscapes of affine fractals, Discrete Wasserstein barycenters: optimal transport for discrete data, Approximating continuous functions on persistence diagrams using template functions, Persistence Flamelets: Topological Invariants for Scale Spaces, Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams, Stabilizing the unstable output of persistent homology computations, ToFU: topology functional units for deep learning, Multiple hypothesis testing with persistent homology, The Persistence Landscape and Some of Its Properties, Iterated Integrals and Population Time Series Analysis, Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis, Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids, A persistence landscapes toolbox for topological statistics, How to Calculate the Barycenter of a Weighted Graph, A random persistence diagram generator

Uses Software

• SW1PerS
• bootstrap

Cites Work

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