Robust support vector model based on bounded asymmetric elastic net loss for binary classification

TL;DR

This paper introduces BAEN-SVM, a robust support vector machine with a novel bounded asymmetric elastic net loss, enhancing noise robustness and geometric stability in binary classification.

Contribution

It proposes a new bounded asymmetric elastic net loss function integrated with SVM, providing robustness, geometric stability, and an efficient solution algorithm.

Findings

Outperforms classical and advanced SVMs on artificial and benchmark datasets.

Demonstrates robustness to noise through bounded influence function.

Provides theoretical guarantees including violation tolerance upper bound and Fisher consistency.

Abstract

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.