Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications

DOI10.1214/20-AOS1988zbMath1468.62303arXiv1811.10178OpenAlexW3145421717WikidataQ114060526 ScholiaQ114060526MaRDI QIDQ2039797

Wolfgang Polonik, Gabriel Chandler

Publication date: 5 July 2021

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.10178

zbMATH Keywords

visualizationVC-classescurse of dimensionalityrandom setnonlinear dimension reductionlocal depthkernel-trickkernelized depth

Mathematics Subject Classification ID

Density estimation (62G07) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Statistics on metric spaces (62R20)

Related Items (1)

Analytical and statistical properties of local depth functions motivated by clustering applications

Uses Software

• SiZer

Cites Work

• Local depth
• On a notion of data depth based on random simplices
• Generalized quantile processes
• Local half-region depth for functional data
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• General notions of statistical depth function.
• Asymptotics for the Tukey depth process, with an application to a multivariate trimmed mean
• Mass estimation
• A weighted localization of halfspace depth and its properties
• A statistical approach to persistent homology
• From Depth to Local Depth: A Focus on Centrality
• 10.1162/15324430260185637
• On a notion of simplicial depth
• SiZer for Exploration of Structures in Curves
• Statistical topological data analysis using persistence landscapes
• [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]
• Unnamed Item

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