Norm-mixed twin support vector machine classifier and its geometric algorithm

In this paper, a novel classifier named norm-mixed twin support vector machine (NMTWSVM) is presented. The main idea in each primal problem of this NMTWSVM is to replace the hinge loss of the other class with the L1-norm-basedL1-norm-based loss, which are obtained from equality constraints, such that each hyperplane is closest to the corresponding class and is as possible as far from the other class. The geometric analysis shows that the dual problems of NMTWSVM can be interpreted as a pair of minimum generalized Mahalanobis-norm problems (MGMNPs) on the two reduced affine hulls (RAHs) composed of two classes of points. As the practical application of the geometric analysis for NMTWSVM, a novel geometric algorithm is suggested based on the geometric properties of RAHs. The experimental results on several artificial and benchmark datasets indicate that the proposed algorithm not only obtains comparable accuracy, but also needs less kernel operations compared with the geometric algorithm of classical support vector machine (SVM).

► It presents a new classifier named NMTWSVM. ► NMTWSVM is interpreted as two minimum generalized Mahalanobis-norm problems. ► It gives the expression of each candidate extreme point of reduced affine hulls. ► It proposes an efficient geometric algorithm for the NMTWSVM.