Smooth support vector machine with rescaled generalized pinball loss for classification

The pinball loss is favored in support vector machines for its robustness against noise. However, its unbounded nature makes it sensitive to outliers. To address this, a rescaled pinball loss offering boundedness has been introduced. Despite this improvement, the model’s performance may be limited due to restricted parameter adjustments, and its non-differentiability constrains optimization methods. Therefore, we propose a novel smooth rescaled generalized pinball loss, which is more flexible and differentiable. This loss is characterized by properties such as asymmetry, non-convexity, sparsity, boundedness, and differentiability. It is applied to support vector machines and is referred to as SRGP-SVM. Since SRGP-SVM involves a differentiable non-convex optimization problem, we employ modified Broyden–Fletcher–Goldfarb–Shanno (BFGS) methods for solving SRGP-SVM to leverage its differentiability. Experimental studies on both synthetic and real datasets demonstrate the model’s performance compared to established models.