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.

中文翻译：

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二次超表面无核最小二乘支持向量回归

对于某些回归问题，我们提出了一种新颖的无核回归函数，称为二次超表面无核最小二乘支持向量回归（QLSSVR）。该方法的任务是找到二次函数作为回归函数，该函数是通过求解具有等式约束的二次规划问题而获得的。基本上，新模型只需要求解线性方程组即可获得最佳解，而不是求解二次规划问题。因此，与标准支持向量回归相比，由于无核且求解了一组线性方程，因此我们的方法非常有效。数值结果表明，在回归标准和CPU时间方面，我们的方法比其他现有的回归方法具有更好的性能。