Support Vector Machines Using Mop/gp Techniques

Abstract. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problems with two class sets, it generalizes linear classifiers into high dimensional feature spaces through nonlinear mappings defined implicitly by kernels in the Hilbert space so that it produces nonlinear classifiers in the original data space. Linear classifiers then are optimized to give the maximal margin separation between the classes. The idea of maximal margin separation was employed in the multi-surface method (MSM) suggested by Mangasarian in 1960’s. Also, linear classifiers using goal programming were developed extensively in 1980’s. This paper proposes a new family of SVM using MOP/GP techniques, and discusses its effectiveness throughout several numerical experiments.