Robust Classification of High-Dimensional Data using Data-Adaptive Energy Distance

TL;DR

This paper introduces robust, tuning-parameter-free classifiers for high-dimensional low sample size data, demonstrating their perfect asymptotic classification and superior performance through theoretical analysis, simulations, and real data applications.

Contribution

It develops novel classifiers for HDLSS data that are robust, parameter-free, and achieve perfect asymptotic classification under general conditions.

Findings

Classifiers are asymptotically perfect in HDLSS regime.

Proposed methods outperform existing classifiers in simulations.

Real data analysis confirms practical advantages.

Abstract

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and analysis of some classifiers that are specifically designed for HDLSS data. These classifiers are free of tuning parameters and are robust, in the sense that they are devoid of any moment conditions of the underlying data distributions. It is shown that they yield perfect classification in the HDLSS asymptotic regime, under some fairly general conditions. The comparative performance of the proposed classifiers is also investigated. Our theoretical results are supported by extensive simulation studies and real data analysis, which demonstrate promising advantages of the proposed classification techniques over several widely recognized methods.