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.

翻译：现有支持向量机（SVM）模型对噪声敏感且缺乏稀疏性，这限制了其性能。为解决这些问题，我们将弹性网损失与稳健损失框架相结合，构建了一个稀疏的$\varepsilon$-不敏感有界非对称弹性网损失，并将其与SVM集成，构建了基于$\varepsilon$-不敏感区间有界非对称弹性网损失的SVM（$\varepsilon$-BAEN-SVM）。$\varepsilon$-BAEN-SVM兼具稀疏性和稳健性。通过证明$\varepsilon$-不敏感带内的样本不是支持向量，验证了其稀疏性。由于影响函数有界，其稳健性在理论上得到了保证。为解决非凸优化问题，我们设计了一种基于裁剪对偶坐标下降的半二次算法。该算法将原问题转化为一系列加权子问题，通过$\varepsilon$参数提高计算效率。在模拟和真实数据集上的实验表明，$\varepsilon$-BAEN-SVM优于传统及现有的稳健SVM。它在噪声环境下很好地平衡了稀疏性和稳健性。统计检验证实了其优越性。在高斯核下，它实现了更高的精度和噪声不敏感性，验证了其有效性和实际价值。