Addressing Heterophily in Graph Anomaly Detection: A Perspective of Graph Spectrum

Graph anomaly detection (GAD) suffers from heterophily — abnormal nodes are sparse so that they are connected to vast normal nodes. The current solutions upon Graph Neural Networks (GNNs) blindly smooth the representation of neiboring nodes, thus undermining the discriminative information of the anomalies. To alleviate the issue, recent studies identify and discard inter-class edges through estimating and comparing the node-level representation similarity. However, the representation of a single node can be misleading when the prediction error is high, thus hindering the performance of the edge indicator. In graph signal processing, the smoothness index is a widely adopted metric which plays the role of frequency in classical spectral analysis. Considering the ground truth Y to be a signal on graph, the smoothness index is equivalent to the value of the heterophily ratio. From this perspective, we aim to address the heterophily problem in the spectral domain. First, we point out that heterophily is positively associated with the frequency of a graph. Towards this end, we could prune inter-class edges by simply emphasizing and delineating the high-frequency components of the graph. Recall that graph Laplacian is a high-pass filter, we adopt it to measure the extent of 1-hop label changing of the center node and indicate high-frequency components. As GAD can be formulated as a semi-supervised binary classification problem, only part of the nodes are labeled. As an alternative, we use the prediction of the nodes to estimate it. Through our analysis, we show that prediction errors are less likely to affect the identification process. Extensive empirical evaluations on four benchmarks demonstrate the effectiveness of the indicator over popular homophilic, heterophilic, and tailored fraud detection methods. Our proposed indicator can effectively reduce the heterophily degree of the graph, thus boosting the overall GAD performance. Codes are open-sourced in https://github.com/blacksingular/GHRN.