Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection

2025-12-21

AI Summary

This study systematically evaluates hyperbolic graph embedding models for graph anomaly detection, aiming to validate their superiority over Euclidean methods in modeling hierarchical and heterogeneous graph structures. We propose the first unified evaluation framework for anomaly detection in hyperbolic space—covering prominent models including P-VAE, HGCN, and HGCAE under the Poincaré ball model—and publicly release HyperAD, a dedicated open-source toolkit to advance practical adoption of hyperbolic graph learning. Experiments demonstrate substantial improvements: P-VAE achieves 94% F1-score on Elliptic, and HGCAE attains 80% on Cora—both significantly outperforming Euclidean baselines such as DOMINANT and GraphSAGE. Our core contributions are threefold: (i) empirical validation of hyperbolic geometry’s enhanced representational capacity for complex anomalous patterns in graphs; (ii) establishment of a reproducible, extensible benchmark; and (iii) open-sourcing of HyperAD to foster standardized evaluation and methodological advancement.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like extit{HGCAE}, extit{(mathcal{P})-VAE}, and extit{HGCN} demonstrates high performance, with extit{(mathcal{P})-VAE} achieving an F1-score of 94% on the extit{Elliptic} dataset and extit{HGCAE} scoring 80% on extit{Cora}. In contrast, Euclidean methods like extit{DOMINANT} and extit{GraphSage} struggle with complex data. The study emphasizes the potential of hyperbolic spaces for improving anomaly detection, and provides an open-source library to foster further research in this field.

Problem

• Survey hyperbolic graph embedding models for anomaly detection
• Evaluate hyperbolic models outperforming Euclidean methods
• Provide open-source library to advance hyperbolic space research

Innovation

• Hyperbolic embeddings outperform Euclidean methods in anomaly detection
• Models like P-VAE achieve high F1-scores on complex datasets
• Open-source library provided to advance hyperbolic graph research