CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

Karish Grover, Geoffrey J. Gordon, Christos Faloutsos

TL;DR: Mixed-curvature autoencoder for unveiling curvature-based (geometric) anomalies in graphs.

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.

Lay Summary:

In today's interconnected world, networks—be it social media platforms, financial systems, or biological interactions—play a pivotal role. Identifying anomalies within these networks is crucial, as they can signify fraudulent activities, misinformation spread, or critical system failures. Traditional detection methods primarily focus on direct connections and node attributes, often overlooking the underlying geometric structure of the network.

Our research introduces CurvGAD, a novel approach that incorporates the concept of curvature from geometry to enhance anomaly detection in graphs. Curvature provides insights into the "shape" or "bending" of the network, revealing areas where the structure deviates from the norm.

CurvGAD operates through two complementary mechanisms: (a) Curvature-Aware Analysis: This component examines the geometric properties of the network, identifying anomalies based on unusual curvature patterns. (b) Structure and Attribute Examination: This part focuses on the traditional aspects—connections and node attributes—ensuring that anomalies not related to geometry are also detected.

By combining these perspectives, CurvGAD not only uncovers anomalies missed by conventional methods but also provides a more interpretable understanding of why certain nodes or connections are deemed anomalous. In evaluations across ten diverse real-world datasets, CurvGAD consistently outperformed existing techniques, highlighting the value of integrating geometric insights into network analysis.

Link To Code: https://github.com/karish-grover/curvgad

Primary Area: Deep Learning->Graph Neural Networks

Keywords: Graph anomaly detection, Riemannian geometry, Mixed-curvature GNN, Spectral graph theory, Ollivier-Ricci curvature, Ricci flow

Submission Number: 9785