Kernel-free double well potential support vector regression

Abstract

In this paper, for the regression problem, a novel kernel-free support vector regression based on the double well potential function (DWPSVR) is proposed.In fact, our model applies a type of kernel-free technique, which directly find a double well potential function to fit data, so that the regression function has geometric diversity. The principle of maximizing G-margin is used to construct our optimization problem, where G-margin is independent of the data and is an approximation of the relative geometric margin. At the same time, the ε-insensitive loss function is introduced. In addition, the primal and dual problems of our model are convex quadratic programming problems, so they can be solved directly. The existence and uniqueness of the optimal solution to both primal and dual problems and some concepts of support vectors are also addressed in theoretical analysis. The 5 artificial and 10 benchmark datasets are utilized in numerical experiments. The experimental results validate that the regression function obtained by our method has geometric diversity and the comprehensive performance of our method outperforms the linear support vector regression model and two kernel-free quadratic regression models.