提出新型抗噪损失函数，提升SVM在噪声数据下的分类稳定性。
Robust support vector model based on bounded asymmetric elastic net loss for binary classification
- 设计有界非对称弹性网络损失，融合SVM增强鲁棒性。
- 理论证明模型具有限制误差容忍度与有界影响函数，抗噪性强。
- 适合处理含异常值的工业分类任务，尤其噪声环境表现优异。
本文提出一种新型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）结合，构建BAEN-SVM模型。该损失函数具有有界性和非对称性，可退化为非对称弹性网合页损失、分位数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存在的几何不合理性问题。通过证明其违反容忍上界（VTUB），表明模型具有几何合理性；进一步推导出其影响函数有界，从理论上保证了对噪声的鲁棒性。同时，模型具备费舍尔一致性，确保泛化能力。由于$ L_{baen} $损失非凸，本文设计了一种基于截断坐标下降的半二次算法，高效求解非凸优化问题。在人工和基准数据集上的实验表明，所提方法优于经典及先进SVM，在噪声环境下性能尤为突出。
原文摘要 · Abstract (English)
In this paper, we propose a novel bounded asymmetric elastic net ($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.
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