ε-Kernel-free soft quadratic surface support vector regression

被引:8
|
作者
Ye, Junyou [1 ,2 ]
Yang, Zhixia [1 ,2 ]
Ma, Mengping [1 ,2 ,3 ]
Wang, Yulan [1 ,2 ]
Yang, Xiaomei [1 ,2 ]
机构
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
[2] Xinjiang Univ, Inst Math & Phys, Urumqi 830046, Peoples R China
[3] China Univ Petr Beijing Karamay, Inst Fac Sci & Arts, Karamay 834000, Peoples R China
基金
中国国家自然科学基金;
关键词
Regression problem; Quadratic programming; epsilon-Quadratic surface support vector regression; BINARY CLASSIFICATION; MACHINE;
D O I
10.1016/j.ins.2022.02.012
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we propose a new regression method called the epsilon-kernel-free soft quadratic surface support vector regression (epsilon-SQSSVR). After converting the n-dimensional regression problem into the (n + 1)-dimensional classification problem, the principle of maximizing the sum of relative geometrical margin of each training point is used to construct our optimization problem, where the quadratic surface is restricted to be a hyperparaboloid by setting both the (n + 1)-th row and (n + 1)-th column of the corresponding matrix to be zero. The existence and uniqueness of the optimal solution to both primal and dual problems are also addressed. It should be pointed out that our model is nonlinear and kernel-free, so it does not need to select kernel function and corresponding parameters. At the same time, it is highly interpretable. In addition, our model is still a quadratic convex programming problem similar to the standard SVR. To visualize the effectiveness of our epsilon-SQSSVR, 6 artificial datasets and 15 benchmark datasets are implemented in numerical experiments. The results show that our method is less time-consuming and as good as the nonlinear standard SVR with kernel function in comprehensive performances. (C) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码:177 / 199
页数:23
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