Error-Bounded Graph Anomaly Loss for GNNs

Graph neural networks (GNNs) have been widely used to learn node representations from graph data in an unsupervised way for downstream tasks. However, when applied to detect anomalies (e.g., outliers, unexpected density), they deliver unsatisfactory performance as existing loss functions fail. For example, any loss based on random walk (RW) algorithms would no longer work because the assumption that anomalous nodes were close with each other could not hold. Moreover, the nature of class imbalance in anomaly detection tasks brings great challenges to reduce the prediction error. In this work, we propose a novel loss function to train GNNs for anomaly-detectable node representations. It evaluates node similarity using global grouping patterns discovered from graph mining algorithms. It can automatically adjust margins for minority classes based on data distribution. Theoretically, we prove that the prediction error is bounded given the proposed loss function. We empirically investigate the GNN effectiveness of different loss variants based on different algorithms. Experiments on two real-world datasets show that they perform significantly better than RW-based loss for graph anomaly detection.