Stochastic Convergence of Persistence Landscapes and Silhouettes

DOI10.1145/2582112.2582128zbMath1395.62187arXiv1312.0308OpenAlexW1983788811WikidataQ59942740 ScholiaQ59942740MaRDI QIDQ4635573

Brittany Terese Fasy, Alessandro Rinaldo, Fréderic Chazal, Fabrizio Lecci, Larry Alan Wasserman

Publication date: 23 April 2018

Published in: Proceedings of the thirtieth annual symposium on Computational geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0308

zbMATH Keywords

bootstrapempirical processespersistent homology

Mathematics Subject Classification ID

Multivariate analysis (62H99) Asymptotic properties of nonparametric inference (62G20) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)

Related Items (20)

Using persistent homology and dynamical distances to analyze protein binding ⋮ Rates of convergence for robust geometric inference ⋮ Unnamed Item ⋮ A framework for differential calculus on persistence barcodes ⋮ Persistence curves: a canonical framework for summarizing persistence diagrams ⋮ On the topological data analysis extensions and comparisons ⋮ Approximating continuous functions on persistence diagrams using template functions ⋮ Persistence Flamelets: Topological Invariants for Scale Spaces ⋮ Functional summaries of persistence diagrams ⋮ The (homological) persistence of gerrymandering ⋮ ToFU: topology functional units for deep learning ⋮ Multiple hypothesis testing with persistent homology ⋮ Nonparametric inference via bootstrapping the debiased estimator ⋮ On the expectation of a persistence diagram by the persistence weighted kernel ⋮ On limit theorems for persistent Betti numbers from dependent data ⋮ Unnamed Item ⋮ Tropical Sufficient Statistics for Persistent Homology ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ A random persistence diagram generator ⋮ Supervised learning with indefinite topological Kernels

This page was built for publication: Stochastic Convergence of Persistence Landscapes and Silhouettes