Optimization-based adversarial perturbations against twin support vector machines

Abstract

To investigate the adversarial perturbations to twin support vector machines (TWSVMs) and hence increase the deviation of separating hyperplanes, we establish an optimization framework for adversarial perturbations of linear TWSVMs by taking the minimal perturbation that may cause the original label changes into account. By transforming the problem into a distance problem from point to intersecting hyperplane, we respectively obtain the explicit solutions to the model for the sample-adversarial perturbations case and for the class-universal adversarial perturbations case. The explicit solution obtained, it increases the interpretability of the conclusion and provides great convenience for calculation. Some numerical experiments are conducted on datasets MNIST and CIFAR-10 with Gaussian noise and trained SVM perturbations, which shows the efficiency of our proposed adversarial perturbations model.