摘要:孪生支持向量机因其简单的模型、快速的训练速度和优秀的性能而受到广泛关注.该算法最初是为解决二分类问题而提出的，不能直接用于解决现实生活中普遍存在的多分类问题.近年来，****们致力于将二分类孪生支持向量机扩展为多分类方法，并提出了多种多分类孪生支持向量机.多分类孪生支持向量机的研究已经取得了一定的进展.主要工作是回顾多分类孪生支持向量机的发展，对多分类孪生支持向量机进行合理归类，分析各个类型的多分类孪生支持向量机的理论和几何意义.以多分类孪生支持向量机的子分类器组织结构为依据，将多分类孪生支持向量机分为：基于"一对多"策略的多分类孪生支持向量机、基于"一对一"策略的多分类孪生支持向量机、基于"一对一对余"策略的多分类孪生支持向量机、基于二叉树结构的多分类孪生支持向量机和基于"多对一"策略的多分类孪生支持向量机.基于有向无环图的多分类孪生支持向量机训练过程与基于"一对一"策略的多分类孪生支持向量机类似，但其决策方式有其特殊的优缺点，因此将其也独立为一类.分析和总结了这6种类型的多分类孪生支持向量机的算法思想、理论基础.此外，还通过实验对比了分类性能.为各种多分类孪生支持向量机之间建立了联系比较，使得初****能够快速理解不同多分类孪生支持向量机之间的本质区别，也对实际应用中选取合适的多分类孪生支持向量机起到一定的指导作用.



Abstract:Twin support vector machines have drawn extensive attention for their simple model, high training speed and good performance. The initial twin support vector machine is designed for binary classification. However, multi class classification problems are also common in practice. In recent years, researchers have devoted themselves to the study of multi class twin support vector machines. Various mulit class twin support vector machines have been proposed. The study of multi class twin support vector machines has made great progress. This paper aims to review the development of multi class twin support vector machines, classify and analyze them with the respect to the basic theories and geometric meanings. According to the structures, the paper divides the machines into the following groups:"one-versus-all" strategy based multi class twin support vector machines, "one-versus-one" strategy based multi class twin support vector machines, binary tree based multi class twin support vector machines, "one-versus-one-versus-rest" strategy based multi class twin support vector machines, and "all-versus-one" strategy based multi class twin support vector machines. Although the training processes of direct acyclic graph based multi class twin support vector machines are much similar with that of "one-versus-one" based approachs, the decision processes have their own characteristics and disadvantages, and therefore they are divided into a separate group. This paper analyzes and summarizes the ideas and theories of different multi class twin support vector machines, and presents experimental results to compare the performances. This review can make it easy for novices to understand the essential differences and help to choose the suitable multi class twin support vector machine for a practical problem.



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