April 2021 Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications
Gabriel Chandler, Wolfgang Polonik
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Ann. Statist. 49(2): 988-1010 (April 2021). DOI: 10.1214/20-AOS1988

Abstract

A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. Based on geometric considerations, we map each pair of data points into a real-valued feature function defined on the unit interval. Further statistical analysis is then based on the collection of feature functions. The potential of the method is illustrated by different applications, including classification and anomaly detection. Connections to other concepts, such as random set theory, localized depth measures and nonlinear dimension reduction, are also explored.

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Gabriel Chandler. Wolfgang Polonik. "Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications." Ann. Statist. 49 (2) 988 - 1010, April 2021. https://doi.org/10.1214/20-AOS1988

Information

Received: 1 December 2019; Revised: 1 June 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1988

Subjects:
Primary: 62G07 , 62GHXX

Keywords: curse of dimensionality , kernelized depth , Kernel-trick , local depth , nonlinear dimension reduction , random set , VC-classes , visualization

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 2 • April 2021
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