Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications
Gabriel Chandler, Wolfgang Polonik
The Annals of Statistics · 2021 · Volume 49 · Issue 2
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.
Keywords
62G07, 62GHXX, curse of dimensionality, kernelized depth, Kernel-trick, local depth, nonlinear dimension reduction, random set, VC-classes, visualization
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