Abstract
In this paper, we propose a novel bounded asymmetric elastic net (L_{baen}) loss function and combine it with the support vector machine (SVM), resulting in the BAEN-SVM. The L_{baen} is bounded and asymmetric and can degrade to the asymmetric elastic net hinge loss, pinball loss, and asymmetric least squares loss. BAEN-SVM not only effectively handles noise-contaminated data but also addresses the geometric irrationalities in the traditional SVM. By proving the violation tolerance upper bound (VTUB) of BAEN-SVM, we show that the model is geometrically well-defined. Furthermore, we derive that the influence function of BAEN-SVM is bounded, providing a theoretical guarantee of its robustness to noise. The Fisher consistency of the model further ensures its generalization capability. Since the \( L_{\text{baen}} \) loss is non-convex, we designed a clipping dual coordinate descent-based half-quadratic algorithm to solve the non-convex optimization problem efficiently. Experimental results on artificial and benchmark datasets indicate that the proposed method outperforms classical and advanced SVMs, particularly in noisy environments.
