Alternative second-order cone programming formulations for support vector classification

This paper presents two novel second-order cone programming (SOCP) formulations that determine a linear predictor using Support Vector Machines (SVMs). Inspired by the soft-margin SVM formulation, our first approach (@x-SOCP-SVM) proposes a relaxation of the conic constraints via a slack variable, penalizing it in the objective function. The second formulation (r-SOCP-SVM) is based on the LP-SVM formulation principle: the bound of the VC dimension is loosened properly using the l"~-norm, and the margin is directly maximized. The proposed methods have several advantages: The first approach constructs a flexible classifier, extending the benefits of the soft-margin SVM formulation to second-order cones. The second method obtains comparable results to the SOCP-SVM formulation with less computational effort, since one conic restriction is eliminated. Experiments on well-known benchmark datasets from the UCI Repository demonstrate that our approach accomplishes the best classification performance compared to the traditional SOCP-SVM formulation, LP-SVM, and to standard linear SVM.