Multiple criteria mathematical programming for multi-class classification and application in network intrusion detection

Multi-class classification problems are harder to solve and less studied than binary classification problems. The goal of this paper is to present a multi-criteria mathematical programming (MCMP) model for multi-class classification. Furthermore, we introduce the concept of e-support vector to facilitate computation of large-scale applications. Instead of finding the optimal solution for a convex mathematical programming problem, the computation of optimal solution for the model requires only matrix computation. Using two network intrusion datasets, we demonstrate that the proposed model can achieve both high classification accuracies and low false alarm rates for multi-class network intrusion classification.