Enhancing GCN robustness against structural attacks via adaptive spectrum filtering

Graph Convolutional Networks (GCNs) are currently the most widely used method for processing graph-structured data. However, recent research has revealed that the performance of GCNs dramatically decreases when confronted with adversarial attacks. This severely hinders their application in security-critical domains. Therefore, the development of GCNs that are resilient to adversarial attacks has emerged as a prominent research focus. Despite this, most current defense models with complex network architectures and optimization objectives are typically designed based on specific feature assumptions or attack manifestations, and do not enhance the inherent robustness of GCNs. They also overlook the changes induced by perturbations of varying intensities and the difference in attack phenomenon across different datasets. In response to this, we have delved into the impact of adversarial attacks on the spectrum, and propose an effective adaptive robust spectrum filter GCN (ASF-GCN). This approach enhances the robustness of GCN models through adaptive filtering without introducing additional conditional assumptions. We theoretically analyze that graphs have different robust frequency intervals under different conditions, validating the necessity of adaptive filtering. Additionally, we elucidate the role of degree distribution and maximum eigenvalue in adaptation. Extensive experiments on real-world graphs reveal that our model surpasses other defense models in overall performance.