  A novel linear classification method that possesses the merits of both the
Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is
proposed in this article. The proposed Distance-weighted Support Vector Machine
method can be viewed as a hybrid of SVM and DWD that finds the classification
direction by minimizing mainly the DWD loss, and determines the intercept term
in the SVM manner. We show that our method inheres the merit of DWD, and hence,
overcomes the data-piling and overfitting issue of SVM. On the other hand, the
new method is not subject to imbalanced data issue which was a main advantage
of SVM over DWD. It uses an unusual loss which combines the Hinge loss (of SVM)
and the DWD loss through a trick of axillary hyperplane. Several theoretical
properties, including Fisher consistency and asymptotic normality of the DWSVM
solution are developed. We use some simulated examples to show that the new
method can compete DWD and SVM on both classification performance and
interpretability. A real data application further establishes the usefulness of
our approach.
