提出新型稀疏鲁棒SVM，有效抗噪且减少支持向量数量。
Sparse $ε$ insensitive zone bounded asymmetric elastic net support vector machines for pattern classification
- 融合弹性网与鲁棒损失，构建新型ε-不敏感带约束的对称损失函数。
- 实验显示在噪声环境下准确率更高，支持向量数显著减少。
- 适合高噪声数据分类任务，尤其适用于需要稀疏性和鲁棒性并重的场景。
现有支持向量机（SVM）模型对噪声敏感且缺乏稀疏性，制约性能表现。为此，本文将弹性网损失与鲁棒损失框架结合，构造一种稀疏的ε-不敏感带边界不对称弹性网损失，并将其集成至SVM中，形成ε-不敏感带边界不对称弹性网损失支持向量机（ε-BAEN-SVM）。该模型兼具稀疏性与鲁棒性：稀疏性由ε-不敏感带内样本非支持向量证明；鲁棒性由影响函数有界理论保证。针对非凸优化问题，设计基于截断对偶坐标下降的半二次算法，将原问题转化为一系列加权子问题，通过ε参数提升计算效率。在模拟与真实数据集上的实验表明，ε-BAEN-SVM优于传统及现有鲁棒SVM，在噪声环境中良好平衡稀疏性与鲁棒性。统计检验验证其优越性。在高斯核下，实现更高准确率与更强抗噪能力，证明其有效性与实用价值。
原文摘要 · Abstract (English)
Existing support vector machines(SVM) models are sensitive to noise and lack sparsity, which limits their performance. To address these issues, we combine the elastic net loss with a robust loss framework to construct a sparse $\varepsilon$-insensitive bounded asymmetric elastic net loss, and integrate it with SVM to build $\varepsilon$ Insensitive Zone Bounded Asymmetric Elastic Net Loss-based SVM($\varepsilon$-BAEN-SVM). $\varepsilon$-BAEN-SVM is both sparse and robust. Sparsity is proven by showing that samples inside the $\varepsilon$-insensitive band are not support vectors. Robustness is theoretically guaranteed because the influence function is bounded. To solve the non-convex optimization problem, we design a half-quadratic algorithm based on clipping dual coordinate descent. It transforms the problem into a series of weighted subproblems, improving computational efficiency via the $\varepsilon$ parameter. Experiments on simulated and real datasets show that $\varepsilon$-BAEN-SVM outperforms traditional and existing robust SVMs. It balances sparsity and robustness well in noisy environments. Statistical tests confirm its superiority. Under the Gaussian kernel, it achieves better accuracy and noise insensitivity, validating its effectiveness and practical value.
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