# Optimization Models and Interpretations for Three Types of Adversarial Perturbations against Support Vector Machines

arXiv: https://arxiv.org/abs/2204.03154 · HTML: https://mlsanity.com/paper/2204.03154/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 7 Apr 2022.

## Builds on (most cited first, 18 of 18)

- [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)
- [Recent Trends in Deep Learning Based Natural Language Processing](https://mlsanity.com/paper/1708.02709/) (2017)
- [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)
- [CD-UAP: Class Discriminative Universal Adversarial Perturbation](https://mlsanity.com/paper/2010.03300/) (2020)
- [Double Targeted Universal Adversarial Perturbations](https://mlsanity.com/paper/2010.03288/) (2020)
- [Active Subspace of Neural Networks: Structural Analysis and Universal Attacks](https://mlsanity.com/paper/1910.13025/) (2019)
- [Recovering Trees with Convex Clustering](https://mlsanity.com/paper/1806.11096/) (2018)
- [A new system-wide diversity measure for recommendations with efficient algorithms](https://mlsanity.com/paper/1812.03030/) (2018)
- [Using Shortlists to Support Decision Making and Improve Recommender System Performance](https://mlsanity.com/paper/1510.07545/) (2015)
- [A Semismooth Newton Method for Support Vector Classification and Regression](https://mlsanity.com/paper/1903.00249/) (2019)
- [An Efficient Augmented Lagrangian Method for Support Vector Machine](https://mlsanity.com/paper/1912.06800/) (2019)

## Built on by (most cited first, 2 of 2)

- [An Efficient Method for Sample Adversarial Perturbations against Nonlinear Support Vector Machines](https://mlsanity.com/paper/2206.05664/) (2022)
- [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 deep neural networks. Most of them are computed by iterations and cannot be interpreted very well. In contrast, little attentions are paid to basic machine learning models such as support vector machines. In this paper, we investigate the optimization models and the interpretations for three types of adversarial perturbations against support vector machines, including sample-adversarial perturbations (sAP), class-universal adversarial perturbations (cuAP) as well as universal adversarial perturbations (uAP). For linear binary/multi classification support vector machines (SVMs), we derive the explicit solutions for sAP, cuAP and uAP (binary case), and approximate solution for uAP of multi-classification. We also obtain the upper bound of fooling rate for uAP. Such results not only increase the interpretability of the three adversarial perturbations, but also provide great convenience in computation since iterative process can be avoided. Numerical results show that our method is fast and effective in calculating three types of adversarial perturbations.