Geometry-Aware Graph Anomaly Detection: Unified Hyperbolic Affinity Learning

Unsupervised graph anomaly detection (UGAD) aims to identify abnormal nodes that deviate from normal patterns without labeled data and has been widely applied to fraud detection, cybersecurity, etc. However, node relationships in real-world graphs often exhibit hierarchical structure. Existing affinity-based graph anomaly detection methods mainly rely on Euclidean spaces to model node relationships, which limits their ability to capture relational differences in complex graph structures. Moreover, different relations are often modeled using different measurement spaces, making it difficult to jointly model multiple relations in complex graph structures. To address these issues, we propose a geometry-aware graph anomaly detection framework via unified hyperbolic affinity learning (UHAL-GAD). Specifically, we first map node representations into a shared Lorentz space and construct a unified hyperbolic affinity based on geodesic distances to learn more discriminative hyperbolic node representations. On this basis, the hyperbolic structural affinity learning module discriminates between normal and abnormal nodes using hyperbolic affinity, while the hyperbolic center affinity constraint module characterizes the hyperbolic center affinity discrepancy of each node with respect to the global Lorentz center. Furthermore, these modules jointly model multiple relations in a unified hyperbolic affinity measurement space. Extensive experiments on multiple graph datasets demonstrate the effectiveness and superior detection performance of UHAL-GAD.