A generalized Gilbert algorithm and an improved MIES for one-class support vector machine

Abstract

This paper is devoted to two issues involved in the one-class support vector machine (OCSVM), i.e., the optimization algorithm and the kernel parameter selection. For appropriate choices of parameters, the primal maximum margin problem of OCSVM is equivalent to a nearest point problem. A generalized Gilbert (GG) algorithm is proposed to solve the nearest point problem. Compared with the algebraic algorithms developed for OCSVM, such as the well-known sequential minimal optimization (SMO) algorithm, the GG algorithm is a novel geometric algorithm that has an intuitive and explicit optimization target at each iteration. Moreover, an improved MIES (IMIES) is developed for the Gaussian kernel parameter selection. IMIES is implemented by constraining the geometric locations of edge and interior sample mappings relative to OCSVM separating hyper-planes. The experimental results on 2-D artificial datasets and benchmark datasets show that IMIES is able to select suitable kernel parameters, and the GG algorithm is computationally more efficient while achieving comparable accuracies to the SMO algorithm.