# Support vector machine and its bias correction in high-dimension, low-sample-size settings

## TL;DR

This paper investigates the asymptotic behavior of support vector machines in high-dimensional, low-sample-size scenarios, revealing bias issues and proposing a bias-corrected SVM that improves classification performance.

## Contribution

The paper introduces a bias-corrected SVM (BC-SVM) tailored for HDLSS settings, enhancing classification accuracy over traditional SVMs.

## Key findings

- Hard-margin SVM achieves consistency with zero misclassification as dimension increases.
- Standard SVMs exhibit significant bias in HDLSS contexts.
- Bias correction improves SVM performance in high-dimensional, low-sample-size data.

## Abstract

In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings. We show that the hard-margin linear SVM holds a consistency property in which misclassification rates tend to zero as the dimension goes to infinity under certain severe conditions. We show that the SVM is very biased in HDLSS settings and its performance is affected by the bias directly. In order to overcome such difficulties, we propose a bias-corrected SVM (BC-SVM). We show that the BC-SVM gives preferable performances in HDLSS settings. We also discuss the SVMs in multiclass HDLSS settings. Finally, we check the performance of the classifiers in actual data analyses.