A Unified Bilevel Model for Adversarial Learning and A Case Study

Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attack is still not quite clear. In this paper, we propose a unified bilevel model for adversarial learning. We further investigate the adversarial attack in clustering models and interpret it from data perturbation point of view. We reveal that when the data perturbation is relatively small, the clustering model is robust, whereas if it is relatively large, the clustering result changes, which leads to an attack. To measure the effect of attacks for clustering models, we analyse the well-definedness of the so-called $\delta$-measure, which can be used in the proposed bilevel model for adversarial learning of clustering models.