Recently, support vector machines (SVMs) based on bounded loss functions have attracted significant attention due to their robustness. In this paper, we propose a novel non-convex, monotonic, and bounded loss function called the \(\epsilon\) -insensitive truncated non-convex ( \(\epsilon\) -TNC) loss, and construct our \(\epsilon\) -TNCSVM model by replacing the hinge loss with the proposed \(\epsilon\) -TNC loss in the standard SVM. The non-convexity and boundedness enhance the robustness of the model, and we innovatively use the influence function of the estimator to demonstrate this theoretically. Monotonicity ensures that the \(\epsilon\) -TNCSVM retains the sparsity of the traditional SVM model. Besides, we demonstrate that \(\epsilon\) -TNCSVM satisfies Fisher consistency and obtains the corresponding generalization error bound based on Rademacher complexity, guaranteeing its good generalization capability. However, the non-convexity of the proposed \(\epsilon\) -TNC loss makes it difficult to optimize. Hence, a non-convex optimization method, the concave-convex procedure (CCCP) technique, is implemented to solve the proposed model. We conduct various experiments to verify the effectiveness of our proposed \(\epsilon\) -TNCSVM model.
