Sparse $\epsilon$ insensitive zone bounded asymmetric elastic net support vector machines for pattern classification

TL;DR

This paper introduces a novel support vector machine model that combines sparsity and robustness using a new elastic net loss framework, improving performance in noisy environments.

Contribution

It proposes the $oldsymbol{ ext{ extepsilon}- ext{BAEN-SVM}}$ model, integrating a sparse, robust elastic net loss with SVM, and develops an efficient half-quadratic optimization algorithm.

Findings

$ ext{ extepsilon}$-BAEN-SVM outperforms traditional SVMs in noisy data.

The model achieves better accuracy and noise insensitivity under Gaussian kernels.

Sparsity is demonstrated by support vectors outside the $ ext{ extepsilon}$-insensitive band.

Abstract

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.