Persistence barcodes versus Kolmogorov signatures: detecting modes of one-dimensional signals

DOI10.1007/s10208-015-9281-9zbMath1367.62086arXiv1404.1214OpenAlexW3105241451MaRDI QIDQ525596

Ulrich Bauer, Hannes Sieling, Axel Munk, Max Wardetzky

Publication date: 5 May 2017

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1214

zbMATH Keywords

critical pointspartial sum processpersistent homologytaut stringsmode huntingbarcodesexponential deviation boundKolmogorov signatures

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Critical points and critical submanifolds in differential topology (57R70)

Related Items (2)

Boundedness and unboundedness in total variation regularization ⋮ Topological data analysis for true step detection in periodic piecewise constant signals

Uses Software

• KernSmooth
• ftnonpar

Cites Work

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• Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data
• Asymptotic Statistics
• Detection with the scan and the average likelihood ratio

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