A Novel Twin-Bounded Support Vector Machine with Smooth Generalized Pinball Loss

We present a one-parameter family of smooth generalized pinball loss functions to overcome the challenges of non-differentiability, noise sensitivity, and resampling instability inherent in traditional loss functions such as hinge loss. These functions make the objective function in the formulation of the support vector machine (SVM) model twice continuously differentiable and improve model performance by reducing noise sensitivity and preserving the sparsity of the solution. Similarly, a novel twin-bounded support vector machine (TBSVM) model with a smooth generalized pinball loss function is obtained. Furthermore, we compare the performance of the TBSVM with the novel type of smooth loss function against other contemporary approaches, offering a comprehensive assessment of its strengths and limitations by conducting an evaluation with UCI datasets. The experimental results show that the proposed model has the best performance in the TBSVM with RBFSampler. Additionally, we prove that the generalized pinball loss function can be approximated by a novel smooth generalized pinball loss function in the uniform norm with arbitrary precision. We further show that the solutions of the proposed SVM and TBSVM models are unique and that they converge to the solutions of the models with non-smooth generalized pinball loss as the parameter approaches zero.