  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.
