National Natural Science Foundation of China (61672522, 61379101); National Key Basic Research Program of China (973) (2013CB329502)
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.