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

arXiv: https://arxiv.org/abs/2206.05664 · HTML: https://mlsanity.com/paper/2206.05664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 12 Jun 2022.

## Builds on (most cited first, 17 of 17)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Recent Trends in Deep Learning Based Natural Language Processing](https://mlsanity.com/paper/1708.02709/) (2017)
- [Attention Mechanisms in Computer Vision: A Survey](https://mlsanity.com/paper/2111.07624/) (2021)
- [Analysis of classifiers' robustness to adversarial perturbations](https://mlsanity.com/paper/1502.02590/) (2015)
- [Fast Feature Fool: A data independent approach to universal adversarial perturbations](https://mlsanity.com/paper/1707.05572/) (2017)
- [NAG: Network for Adversary Generation](https://mlsanity.com/paper/1712.03390/) (2017)
- [Art of singular vectors and universal adversarial perturbations](https://mlsanity.com/paper/1709.03582/) (2017)
- [CD-UAP: Class Discriminative Universal Adversarial Perturbation](https://mlsanity.com/paper/2010.03300/) (2020)
- [An Ambient Intelligence-Based Human Behavior Monitoring Framework for Ubiquitous Environments](https://mlsanity.com/paper/2106.15609/) (2021)
- [Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines](https://mlsanity.com/paper/2204.03154/) (2022)

## Built on by (most cited first, 1 of 1)

- [Bilevel Models for Adversarial Learning and A Case Study](https://mlsanity.com/paper/2510.25121/) (2025)

## Abstract (arXiv)

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.