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

•We give asymptotic properties of the SVM in the HDLSS context.•We derive the bias term in the SVM and show that the performance of the SVM is affected by the bias directly.•We propose a bias-corrected SVM (BC-SVM) and show that the BC-SVM improves the performance of the SVM successfully in the HDLSS context.

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.