Graph Convolutional Networks (GCNs) have fueled a surge of interest due to their superior performance on graph learning tasks, but are also shown vulnerability to adversarial attacks. In this paper, an effective graph structural attack is investigated to disrupt graph spectral filters in the Fourier domain. We define the spectral distance based on the eigenvalues of graph Laplacian to measure the disruption of spectral filters. We then generate edge perturbations by simultaneously maximizing a task-specific attack objective and the proposed spectral distance. The experiments demonstrate remarkable effectiveness of the proposed attack in the white-box setting at both training and test time. Our qualitative analysis shows the connection between the attack behavior and the imposed changes on the spectral distribution, which provides empirical evidence that maximizing spectral distance is an effective manner to change the structural property of graphs in the spatial domain and perturb the frequency components in the Fourier domain.

翻译：图形革命网络(GCNs)因其在图表学习任务方面的优异性能而激发了人们的兴趣,但也表现出很容易受到对抗性攻击。在本文中,对有效的图形结构攻击进行了调查,以破坏Fourier域的图形光谱过滤器。我们根据图Laplacian的光值来定义光谱距离,以测量光谱过滤器的中断。我们随后通过同时最大限度地实现任务特定攻击目标和拟议的光谱距离,产生边缘扰动。实验表明,在培训和测试时,白箱设置中拟议的攻击非常有效。我们的质量分析显示攻击行为与光谱分布强制变化之间的联系,它提供了经验证据,证明最大限度扩大光谱距离是改变空间域图的结构属性的有效方式,并扰动了Fourier域的频率组成部分。