This article focuses on a specific family of classifiers called nonparallel support vector classifiers (NPSVCs). Different from typical classifiers, the training of an NPSVC involves the minimization of multiple objectives, resulting in the potential concerns of feature suboptimality and class dependence. Consequently, no effective learning scheme has been established to improve NPSVCs' performance through representation learning, especially deep learning. To break this bottleneck, we develop NPSVC++ based on multiobjective optimization, enabling the seamless learning of NPSVC and its features. By pursuing Pareto optimality, NPSVC++ theoretically ensures feature optimality across different classes, thus effectively overcoming these two issues mentioned above. A general learning procedure via duality optimization is proposed, based on which we provide two applicable instances, K-NPSVC++ and D-NPSVC++. Moreover, the convergence analysis of the proposed algorithm is provided. The experiments show their superiority over the existing methods and verify the efficacy of NPSVC++.
Zhang et al. (Thu,) studied this question.