Topology Augmented Multi-Band and Multi-Scale Filtering for Graph Anomaly Detection

Graph Anomaly Detection (GAD) has gained significant attention in areas such as financial risk control and social network security, becoming a critical research problem. Vanilla Graph Neural Networks (GNNs), a popular method for graph modeling, are known to perform poorly in GAD due to the assumption of homophily preferences. This article argues that the issue lies in the insufficient feature extraction ability caused by their single filtering property (low-pass filtering) and revealing the effectiveness of multi-band filtering to deal with GAD. From this, we note two other overlooked issues: (1) How can multi-band band-pass filtering further fuse multi-scale neighborhood information? (2) Adaptation between raw attributes of nodes and graph filters (graph topology). The former bridges the respective advantages of spectral domain and spatial domain, and the latter is an important bottleneck for the encoding capacity of the filters. To address these, we propose a new GAD method, Graph Perturbed Networks (GraphPN). Each hidden layer of GraphPN is a band-pass filter, enabling multi-band and multi-scale filtering through simple stacking and skip connections. We analyze its spectral locality and spatial locality to provide theoretical support. Additionally, GraphPN is supplemented with a tailored feature activation module to complete the adaptation of the above two. This module readjusts node indices and decouples graph convolution, introducing rich topological information to node attributes. In addition to further enhancing detection performance, another possibly counter-intuitive effect is that the distinguishability of the two classes of nodes is improved even before filtering. The proposed method performs well in real-world datasets compared with the current state-of-the-art baselines, which fully demonstrates its superiority. Codes are available at https://github.com/Thankstaro/GraphPN .