Abstract: For multi-class classification, a new hypersphere SVM algorithm is given in this paper, and named as General Maximal-interval Hypersphere SVM（GMHSVM）. In this algorithm, positive and negative samples are separated by two different concentric hyperspheres, the model target is to maximize the difference of two hyperspheres’ radious, which represents the discriminant information of two classes, meanwhile, fuzzy membership is introduced to improve the decision rules of hypersphere SVM, which makes up the voting-decision flaw of two-class classifier. Related properties are obtained by theoretical analysis, simulation experiment results show the effectiveness of the proposed method.

Key words: Support Vector Machine（SVM）, Support Vector Data Description（SVDD）, Maximal-interval Minimal-
volume Hypersphere SVM（MMHSVM）, fuzzy membership

摘要： 针对多类分类问题，提出一种超球支持向量机算法——广义最大间隔球形支持向量机，该算法利用两同心超球将正负类样本分隔开来，最大化两超球半径的差异，从而挖掘正负类样本的鉴别信息，同时对超球类支持向量机算法判决规则进行改进，引入模糊隶属度补充判决，弥补二类分类器投票决策的缺陷。理论分析了算法的相关性质，通过仿真实验验证了该算法的有效性。

关键词: 支持向量机, 支持向量数据描述, 最大间隔最小体积球型支持向量机, 模糊隶属度