Robust and Sparse L_P-Norm Support Vector Regression

Abstract

A robust and sparse L_p-norm support vector regression (L_p-RSVR) is proposed in this paper. The implementation of feature selection in our L_p-RSVR not only preserves the performance of regression but also improves its robustness. The main characteristics of L_p-RSVR are as follows: (i) By using the absolute constraint, L_p-RSVR performs robustly against outliers. (ii) L_p-RSVR ensures that useful features are selected based on theoretical analysis. (iii) Based on the feature-selection results, nonlinear L_p-RSVR can be used when data is structurally nonlinear. Experimental results demonstrate the superiorities of the proposed L_p-RSVR in both feature selection and regression performance as well as its robustness.