Novel Feature Selection Method for Nonlinear Support Vector Regression

The development of sparse techniques presents a major challenge to complex nonlinear high-dimensional data. In this paper, we propose a novel feature selection method for nonlinear support vector regression, called FS-NSVR, which first attempts to solve the nonlinear feature selection problem in the regression technology field. FS-NSVR preserves the representative features selected in the complex nonlinear system due to its use of a feature selection matrix in the original space. FS-NSVR is a challenging mixed-integer programming problem that is solved efficiently by using an alternate iterative greedy algorithm. Experimental results on three artificial datasets and five real-world datasets confirm that FS-NSVR effectively selects representative features and discards redundant features in a nonlinear system. FS-NSVR outperforms L1-norm support vector regression, L1-norm least squares support vector regression, and Lp-norm support vector regression on both feature selection ability and regression efficiency.