Robust support vector machines under label noise: an efficient signed reformulation approach

Ahmadi, Ehsan; Fallahi, Saeed

doi:10.22103/jmmr.2026.27092.1962

Robust support vector machines under label noise: an efficient signed reformulation approach

Articles in Press

Document Type : Research Paper

Authors

Ehsan Ahmadi ¹

Saeed Fallahi ²

¹ Department of Computer Engineering, Salman Farsi University of Kazerun, Kazerun, Iran

² Department of Mathematics and Computer Science, Salman Farsi University of Kazerun, Kazerun, Iran

10.22103/jmmr.2026.27092.1962

Abstract

‎This paper presents a new mixed integer optimization reformulation for robust binary support vector machines under symmetric label noise‎. ‎Recent work has addressed this issue through mixed integer programming formulations that incorporate label uncertainty via binary decision variables‎. ‎Representative approaches‎, ‎such as CDRESVM and DRESVM‎, ‎introduce mechanisms for label correction in the dual formulation‎. ‎Despite their modeling flexibility‎, ‎these methods depend on Big-$M$ constraints and auxiliary variables‎, ‎which often result in weak continuous relaxations‎, ‎numerical instability‎, ‎and increased computational burden‎. ‎To address these shortcomings‎, ‎a new formulation‎, ‎termed Signed DRESVM (SD-DRESVM)‎, ‎is developed‎. ‎The model is based on a signed decomposition in which each dual variable is expressed as the difference of two nonnegative components‎, ‎governed by a single binary variable‎.
‎This construction eliminates the Big-$M$ parameters and auxiliary coupling constraints required by CDRESVM‎, ‎yielding a more compact mixed-integer optimization formulation with a simpler constraint structure while preserving its label correction mechanism‎. ‎Experimental results on sixteen benchmark datasets with symmetric label noise demonstrate that the proposed formulation consistently achieves classification performance that is statistically comparable to the strongest existing robust SVM formulations while substantially improving computational efficiency‎. ‎These results indicate that the proposed signed reformulation preserves predictive robustness while providing a more compact and computationally attractive optimization model‎.

Keywords

Robust support vector machine

label noise

mixed-integer optimization

signed decomposition

Subjects

Optimization

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