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

arXiv: https://arxiv.org/abs/1702.08019 · HTML: https://mlsanity.com/paper/1702.08019/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2017.

## Built on by (most cited first, 3 of 3)

- [New Hard-thresholding Rules based on Data Splitting in High-dimensional Imbalanced Classification](https://mlsanity.com/paper/2111.03306/) (2021)
- [Robust Federated Learning via Byzantine Filtering over Encrypted Updates](https://mlsanity.com/paper/2602.05410/) (2026)
- [Asymptotic Properties of Support Vector Machines in High-Dimension, Low-Sample-Size Settings under a Spiked Model](https://mlsanity.com/paper/2609.39173/) (2026)

## Abstract (arXiv)

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.