A Novel and Principled Multiclass Support Vector Machine

Support vector machines (SVMs) have been demonstrated very efficient for binary classification problems; however, computationally efficient and effective multiclass SVMs are still missing. Most existing multiclass SVM classifiers are constructed either by combining multiple binary SVM classifiers, which often perform moderately for some problems, or by converting multiclass problems into one single optimization problem, which is unfortunately computationally expensive. To address these issues, a novel and principled multiclass SVM based on geometric properties of hyperspheres, termed SVMGH, is proposed in this paper. Different from existing SVM‐based methods that seek a cutting hyperplane between two classes, SVMGH draws the discriminative information of each class by constructing a minimum hypersphere containing all class members, and then defines a label function based on the geometric properties of the minimum hyperspheres. We prove theoretically the geometric properties of the minimum hyperspheres to guarantee the validation of SVMGH. The computational efficiency is enhanced by a data reduction strategy as well as a fast training method. Experimental results demonstrate that the proposed SVMGH shows better performance and higher computational efficiency than the state of the art on multiclassification problems while maintaining comparable performance and efficiency on binary classification problems.