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.

翻译：本文提出了一种新颖的有界非对称弹性网络（\(L_{baen}\)）损失函数，并将其与支持向量机（SVM）相结合，得到了BAEN-SVM模型。\(L_{baen}\)损失具有有界性和非对称性，并可退化为非对称弹性网络铰链损失、pinal损失和非对称最小二乘损失。BAEN-SVM不仅能有效处理噪声污染数据，还能解决传统SVM中的几何不合理性。通过证明BAEN-SVM的违规容忍上界（VTUB），我们表明该模型在几何上是良定义的。此外，我们推导出BAEN-SVM的影响函数是有界的，这为其对噪声的鲁棒性提供了理论保证。模型的Fisher一致性进一步确保了其泛化能力。鉴于\(L_{\text{baen}}\)损失是非凸的，我们设计了一种基于裁剪对偶坐标下降的半二次算法来高效求解该非凸优化问题。在人工数据集和基准数据集上的实验结果表明，所提方法优于经典和先进的SVM，特别是在噪声环境下表现更佳。