SD-Attack: Targeted Spectral Attacks on Graphs

Graph learning (GL) models have been applied in various predictive tasks on graph data. But, similarly to other machine learning models, GL models are also vulnerable to adversarial attacks. As a powerful attack method on graphs, spectral attack jeopardizes the eigenvalues or eigenvectors of the graph topology-related matrices (e.g., graph adjacency matrix and graph Laplacian matrix) due to their inherent connections to certain structural properties of the underlying graph. However, most existing spectral attack methods focus on damaging the global graph structural properties and can hardly perform effective attacks on a target node. In this paper, we propose a novel targeted spectral attack method that can perform model-agnostic attacks effectively on the local structural properties of a target node. First, we define a novel node-specific metric—spectral density distance, which measures the difference of the local structural properties for the same target node between two different graph topologies. Then, we conduct attacks by maximizing the spectral density distance between the graphs before and after perturbation. Additionally, we also develop an effective strategy to improve attack efficiency by using the eigenvalue perturbation theory. Experimental results on three widely used datasets demonstrate the effectiveness of our proposed approach.