Haiyan Du

Haiyan Du, Hu Yang

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.

Haiyan Du, Hu Yang

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.