Abstract: This paper proposes a nonparallel ε-band support vector regression (NSVR) method, in which an ε-up hyperplane and an ε-down hyperplane are constructed via a pair of convex quadratic programming (QP) problems and the final regression function is derived. However, it is worth mentioning that the size of each QP problem is a half that of support vector regression (SVR). Compared with twin support vector regression (TSVR), although they are both looking for two nonparallel hyperplanes to construct the final regression function, the geometrical meaning of NSVR is more close to SVR. The experimental results indicate that NSVR has not only a good generalization performance but also a high speed.

Key words: machine learning, support vector regression (SVR), twin support vector regression (TSVR)

摘要： 提出了一个非平行ε-带支持向量回归机，它通过一对凸二次规划问题确定一个ε-不敏感的上界超平面和一个ε-不敏感的下界超平面，从而得到最终的回归函数。每个凸二次规划问题的规模是传统的支持向量回归机的一半。与双支持向量机相比，虽然它们都是寻找两个不一定平行的超平面来构造最终的回归函数，但是非平行ε-带支持向量回归机的几何意义更接近传统的支持向量回归机。数据实验结果也表明，非平行ε-带支持向量回归机不仅具有良好的泛化性能，而且速度快。

关键词: 机器学习, 支持向量回归机（SVR）, 双支持向量回归机（TSVR）