CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

• URL: http://arxiv.org/abs/2502.08605v2
• Date: Wed, 04 Jun 2025 20:09:51 GMT
• Title: CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection
• Authors: Karish Grover, Geoffrey J. Gordon, Christos Faloutsos,
• Abstract summary: We propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies.<n>CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability.<n>Experiments over 10 real-world datasets demonstrate an improvement of up to 6.5% over state-of-the-art GAD methods.
• Score: 23.643189106137008
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on structural and attribute-level anomalies. To this end, we propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies. CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability: (1) Curvature-equivariant geometry reconstruction, which focuses exclusively on reconstructing the edge curvatures using a mixed-curvature, Riemannian encoder and Gaussian kernel-based decoder; and (2) Curvature-invariant structure and attribute reconstruction, which decouples structural and attribute anomalies from geometric irregularities by regularizing graph curvature under discrete Ollivier-Ricci flow, thereby isolating the non-geometric anomalies. By leveraging curvature, CurvGAD refines the existing anomaly classifications and identifies new curvature-driven anomalies. Extensive experimentation over 10 real-world datasets (both homophilic and heterophilic) demonstrates an improvement of up to 6.5% over state-of-the-art GAD methods. The code is available at: https://github.com/karish-grover/curvgad.

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