# On Generalizations of Some Distance Based Classifiers for HDLSS Data

arXiv: https://arxiv.org/abs/1902.03295 · HTML: https://mlsanity.com/paper/1902.03295/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Robust Classification of High-Dimensional Data using Data-Adaptive Energy Distance](https://mlsanity.com/paper/2306.13985/) (2023)
- [On high-dimensional modifications of the nearest neighbor classifier](https://mlsanity.com/paper/2407.05145/) (2024)
- [Multi-view mid fusion: a universal approach for learning in an HDLSS setting](https://mlsanity.com/paper/2507.06026/) (2025)
- [A scalable version of MADD for big-data classification](https://mlsanity.com/paper/2607.08334/) (2026)

## Abstract (arXiv)

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.