Abstract: In this paper Least Square Twin Support Vector Regression（LSTSVR） is proposed, which is formulated via the idea of Twin Support Vector Regression（TSVR）. LSTSVR breaks the idea which [ε]-band is constructed by two parallel hyperplanes in traditional Support Vector Regression（SVR）. Actually, LSTVR employes two non-parallel hyperplanes to construct the [ε]-band, in which each hyperplane determinates a half [ε]-bond, and obtain the final regression. So the regression function fits the distribution of dataset and the algorithm has better generalization ability. In addition, in LSTSVR, the main computing cost is to solve two smaller systems of linear equations, so the computational complexity is low. The experimental results indicate that the proposed algorithm has certain advantage in generalization ability and computational efficiency.

Key words: regression problem, support vector regression, twin support vector regression, least square twin support vector regression

摘要： 提出了一个最小二乘双支持向量回归机，它是在双支持向量回归机基础之上建立的，打破了标准支持向量回归机利用两条平行超平面构造[ε]带的思想。事实上，它是利用两条不一定平行的超平面构造[ε]带，每条超平面确定一个半[ε]-带，从而得到最终的回归函数，这使该回归函数更符合数据本身的分布情况，回归算法有更好的推广能力。另外，最小二乘双支持向量机只需求解两个较小规模的线性方程组就能得到最后的回归函数，其计算复杂度相对较低。数值实验也表明该回归算法在推广能力和计算效率上有一定的优势。

关键词: 回归问题, 支持向量回归机, 双支持向量回归机, 最小二乘双支持向量回归机