Support vector machine and its bias correction in high-dimension, low-sample-size settings
This work addresses a specific problem in machine learning for high-dimensional data analysis, offering an incremental improvement to SVM methods.
The paper tackles the bias and performance issues of support vector machines (SVM) in high-dimension, low-sample-size (HDLSS) settings by proposing a bias-corrected SVM (BC-SVM), which shows preferable performances in these challenging conditions.
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.