CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

TL;DR

CurvGAD introduces a novel graph autoencoder leveraging intrinsic curvature to detect geometric anomalies in complex networks, outperforming existing methods by up to 6.5% on diverse datasets.

Contribution

It proposes a mixed-curvature graph autoencoder that incorporates curvature-based geometric anomaly detection and decouples structural and attribute anomalies from geometric irregularities.

Findings

Achieves up to 6.5% improvement over state-of-the-art GAD methods.

Effectively identifies curvature-driven anomalies in real-world datasets.

Enhances anomaly interpretability through dual pipelines.

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.