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

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 $\mathit{\text{HGCAE}}$, $\mathcal{P}\mathit{\text{-VAE}}$, and $\mathit{\text{HGCN}}$ demonstrates high performance, with $\mathcal{P}\mathit{\text{-VAE}}$ achieving an F1-score of 94% on the $\mathit{\text{Elliptic}}$ dataset and $\mathit{\text{HGCAE}}$ scoring 80% on $\mathit{\text{Cora}}$. In contrast, Euclidean methods like $\mathit{\text{DOMINANT}}$ and $\mathit{\text{GraphSage}}$ 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.