MULTISCALE GEOMETRIC FEATURE EXTRACTION FOR HIGH-DIMENSIONAL AND NON-EUCLIDEAN DATA WITH APPLICATIONS

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.

Automated summary

This paper proposes a method for extracting multiscale geometric features from a data cloud, and demonstrates its potential in various applications such as classification and anomaly detection. It also explores connections to other concepts such as random set theory, localized depth measures, and nonlinear dimension reduction.