支持向量机(SVM)是当前公认最有效的机器学习方法之一。非平行支持向量机将SVM构造的“平行超平面”推广至“非平行超平面”，是SVM方法新的突破。它在处理“交叉型”和“异方差噪声型”数据问题上突显出了良好的泛化能力,进而得到了很多学者关注和后续研究。然而，非平行支持向量机的研究还很不充分，尤其是其最优化理论和模型方面的研究还很欠缺。本课题拟在若干前期基础上来研究非平行支持向量机,主要包括：(1) 提出具有最大间隔和统一度量的非平行支持向量机模型，并给出相关的理论证明；(2) 针对异分布结构数据，引入结构正则化惩罚，捕获数据聚类结构信息，构建基于“簇粒度”的非平行支持向量机模型；(3) 结合超松弛(SOR)技术与光滑(Smoothing)技术对以上模型提出具有稀疏性的快速求解算法。本课题将为非平行支持向量机的研究提供理论、方法和技术支持。

Support vector machine (SVM) has been recognized as one of the most effective learning methods in the machine learning community. As a new breakthrough, nonparallel support vector machine relaxes the universal requirement that the hyperplanes generated by SVM should be parallel, resulting in excellent at dealing with “xor” and “heteroscedastic noise” problems. Thus, methods of constructing nonparallel support vector machine has been extensively studied. However, compared with SVM, it still has many challenges, especially in its optimization theory and modeling. Based on our preliminary works, we study the nonparallel support vector machine from the following aspects: (1) we will propose a novel nonparallel support vector machine with maximum margin and unified metric, and further give its theoretical framework. (2) For the heteroscedastic distribution structure problem, we will construct a cluster-based structure nonparallel support vector machine via structure regularization penalty. (3) Combing with the over-relaxation and smoothing techniques, fast and sparse solving algorithms will be further designed for the above models. The goal of our project is provide the theory, methods and technical support for nonparallel support vector machine.