Non-smooth optimization algorithm to solve the LINEX soft support vector machine

The Support Vector Machine (SVM) is a cornerstone of machine learning algorithms. This paper proposes a novel cost-sensitive model to address the challenges of class-imbalanced datasets inherent to SVMs. Integrating soft-margin SVM with the asymmetric LINEX loss function, this approach effectively tackles issues in scenarios with noisy data or overlapping classes. The LINEX loss function, which resembles the hinge and square loss functions, facilitates efficient model training with reduced sample penalties. Despite the resulting model’s nonsmooth nature due to a constraint inequality, optimization is achieved using a Primal–Dual method, capitalizing on the convexity of the optimization function. This method enhances the model’s noise robustness while preserving its original form. Extensive experiments validate the model’s effectiveness, showcasing its superiority over traditional methods. Statistical tests further corroborate these findings.