An Efficient Method for Sample Adversarial Perturbations against Nonlinear Support Vector Machines

2022/06/12 by Su Wen, Qingna Li, Su, Wen +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #Bacillus and Francisella bacterial research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2206.05664

openalex publication_date 2022/06/12 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

Abstract

Adversarial perturbations have drawn great attentions in various machine learning models. In this paper, we investigate the sample adversarial perturbations for nonlinear support vector machines (SVMs). Due to the implicit form of the nonlinear functions mapping data to the feature space, it is difficult to obtain the explicit form of the adversarial perturbations. By exploring the special property of nonlinear SVMs, we transform the optimization problem of attacking nonlinear SVMs into a nonlinear KKT system. Such a system can be solved by various numerical methods. Numerical results show that our method is efficient in computing adversarial perturbations.

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