Wei Dong, Yang Zhixia, Ye Junyou, Yang Xue
College of Mathematics and Systems Science, Xinjiang University, Urumuqi 830046, China.
Institute of Mathematics and Physics, Xinjiang University, Urumuqi 830046, China.
Entropy (Basel). 2023 Jul 7;25(7):1030. doi: 10.3390/e25071030.
In this paper, a kernel-free quadratic surface support vector regression with non-negative constraints (NQSSVR) is proposed for the regression problem. The task of the NQSSVR is to find a quadratic function as a regression function. By utilizing the quadratic surface kernel-free technique, the model avoids the difficulty of choosing the kernel function and corresponding parameters, and has interpretability to a certain extent. In fact, data may have a priori information that the value of the response variable will increase as the explanatory variable grows in a non-negative interval. Moreover, in order to ensure that the regression function is monotonically increasing on the non-negative interval, the non-negative constraints with respect to the regression coefficients are introduced to construct the optimization problem of NQSSVR. And the regression function obtained by NQSSVR matches this a priori information, which has been proven in the theoretical analysis. In addition, the existence and uniqueness of the solution to the primal problem and dual problem of NQSSVR, and the relationship between them are addressed. Experimental results on two artificial datasets and seven benchmark datasets validate the feasibility and effectiveness of our approach. Finally, the effectiveness of our method is verified by real examples in air quality.
本文针对回归问题提出了一种具有非负约束的无核二次曲面支持向量回归方法（NQSSVR）。NQSSVR的任务是找到一个二次函数作为回归函数。通过利用二次曲面无核技术，该模型避免了选择核函数及其相应参数的困难，并在一定程度上具有可解释性。事实上，数据可能具有先验信息，即响应变量的值会随着解释变量在非负区间内的增长而增加。此外，为了确保回归函数在非负区间上单调递增，引入了关于回归系数的非负约束来构建NQSSVR的优化问题。并且NQSSVR得到的回归函数与该先验信息相匹配，这在理论分析中已得到证明。此外，还讨论了NQSSVR原始问题和对偶问题解的存在性和唯一性，以及它们之间的关系。在两个人工数据集和七个基准数据集上的实验结果验证了我们方法的可行性和有效性。最后，通过空气质量的实际例子验证了我们方法的有效性。
