Asymptotic properties of distance-weighted discrimination and its bias correction for high-dimension, low-sample-size data

While distance-weighted discrimination (DWD) was proposed to improve the support vector machine in high-dimensional settings, it is known that the DWD is quite sensitive to the imbalanced ratio of sample sizes. In this paper, we study asymptotic properties of the DWD in high-dimension, low-sample-size (HDLSS) settings. We show that the DWD includes a huge bias caused by a heterogeneity of covariance matrices as well as sample imbalance. We propose a bias-corrected DWD (BC-DWD) and show that the BC-DWD can enjoy consistency properties about misclassification rates. We also consider the weighted DWD (WDWD) and propose an optimal choice of weights in the WDWD. Finally, we discuss performances of the BC-DWD and the WDWD with the optimal weights in numerical simulations and actual data analyses.

Automated summary

The DWD is sensitive to imbalanced sample sizes in high-dimensional, low-sample-size settings. The proposed BC-DWD corrects for this bias and shows consistency in misclassification rates. Optimal weights are also proposed for the WDWD to improve its performance.