Study on kernel-based Wilcoxon classifiers

Nonparametric Wilcoxon regressors, which generalize the rank-based Wilcoxon approach for linear parametric regression problems to nonparametric neural networks, were recently developed aiming at improving robustness against outliers in nonlinear regression problems. It is natural to investigate if the Wilcoxon approach can also be generalized to nonparametric classification problems. Motivated by support vector classifiers (SVCs), we propose in this paper a novel family of classifiers, called kernel-based Wilcoxon classifiers (KWCs), for nonlinear classification problems. KWC has the same functional form as that of SVC, but with a totally different objective function. Simple weight updating rules based on gradient projection will be provided. Simulation results show that performances of KWCs and SVCs are about the same.