Quadratic hyper-surface kernel-free least squares support vector regression

We present a novel kernel-free regressor, called quadratic hyper-surface kernel-free least squares support vector regression (QLSSVR), for some regression problems. The task of this approach is to find a quadratic function as the regression function, which is obtained by solving a quadratic programming problem with the equality constraints. Basically, the new model just needs to solve a system of linear equations to achieve the optimal solution instead of solving a quadratic programming problem. Therefore, compared with the standard support vector regression, our approach is much efficient due to kernel-free and solving a set of linear equations. Numerical results illustrate that our approach has better performance than other existing regression approaches in terms of regression criterion and CPU time.