A new fuzzy maximal-margin spherical-structured multi-class support vector machine

Support vector machines (SVMs), initially proposed for two-class classification problems, have been very successful in pattern recognition problems. For multi-class classification problems, the standard hyperplane-based SVMs are made by constructing and combining several hyperplanes. Instead of using maximal-margin hyperplanes, maximal-margin hyperspheres that each tightly encloses all examples from one class but excludes all examples from the rest class can be used. Since the class-specific 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 fuzzy set theory into the maximal-margin spherical-structured multi-class SVMs (MSM-SVM). The parameters to be estimated in the MSM-SVM, such as the components within the spherical center vector and the radius, are set to be the fuzzy numbers. This integration preserves the benefits of SVMs learning theory and fuzzy set theory, where the SVMs learning theory characterizes the properties of learning machines which enable them to effectively generalize the unseen data and the fuzzy set theory might be very useful for finding a fuzzy structure in an evaluation system. Experimental results show that the proposed method performs well on benchmark datasets.