文件名称：Maximal Margin Sphere-Structured Multi-class Support Vector Machine
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Support Vector Machine
Appl Intell (2009) 30: 98–111 DOI 10.1007/s10489-007-0101-z A new maximal-margin spherical-structured multi-class support vector machine Pei-Yi Hao · Jung-Hsien Chiang · Yen-Hsiu Lin Published online: 18 October 2007 © Springer Science+Business Media, LLC 2007 Abstract Support vector machines (SVMs), initially proposed for two-class classification problems, have been very successful in pattern recognition problems. For multiclass classification problems, the standard hyperplane-based SVMs are made by constructing and combining several maximal-margin hyperplanes, and each class of data is confined into a certain area constructed by those hyperplanes. Instead of using hyperplanes, hyperspheres that tightly enclosed the data of each class can be used. Since the classspecific hyperspheres are constructed for each class separately, the spherical-structured SVMs can be used to deal with the multi-class classification problem easily. In addition, the center and radius of the class-specific hypersphere characterize the distribution of examples from that class, and may be useful for dealing with imbalance problems. In this paper, we incorporate the concept of maximal margin into the spherical-structured SVMs. Besides, the proposed approach has the advantage of using a new parameter on controlling the number of support vectors. Experimental results show that the proposed method performs well on both artificial and benchmark datasets.