Robust Optimization Models for Nonparallel Support Vector Machine

Abstract

To address the classification performance degradation caused by noise-contaminated data in real-world scenarios, we propose a robust Nonparallel Support Vector Machine (NPSVM) framework based on uncertainty sets. The suggested framework innovatively overcomes the limitation of precise-label dependency in traditional methods by employing two tactically deployed nonparallel hyperplanes that ensure robust classification performance in noisy environments. Four fundamental innovations distinguish our approach. First, the multi-parameter penalty mechanism compensates for class imbalance, improving classification accuracy. Second, the $\epsilon$-insensitive loss function provides inherent noise resistance and preserves model sparsity. Third, rigorous robustness is ensured by our convex optimization-based uncertainty quantification employing hyper-rectangle and hyper-ellipsoid sets. Finally, the proposed model has computational efficiency by solving two smaller convex sub-problems. Experimental validation on UCI benchmark datasets demonstrates the superior performance of our method compared to conventional algorithms with the hyper-ellipsoidal uncertainty set-based classifier exhibiting particularly outstanding results.