MULTISCALE GEOMETRIC FEATURE EXTRACTION FOR HIGH-DIMENSIONAL AND NON-EUCLIDEAN DATA WITH APPLICATIONS
成果类型：
Article
署名作者：
Chandler, Gabriel; Polonik, Wolfgang
署名单位：
Claremont Colleges; Pomona College; University of California System; University of California Davis
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/20-AOS1988
发表日期：
2021
页码：
988-1010
关键词：
摘要：
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.