A second-order cone programming formulation for twin support vector machines

Second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.