Title: Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection
ArXiv ID: 2512.18826
Date: 2025-12-21
Authors: Souhail Abdelmouaiz Sadat, Mohamed Yacine Touahria Miliani, Khadidja Hab El Hames, Hamida Seba, Mohammed Haddad
📝 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 \textit{HGCAE}, \textit{\(\mathcal{P}\)-VAE}, and \textit{HGCN} demonstrates high performance, with \textit{\(\mathcal{P}\)-VAE} achieving an F1-score of 94\% on the \textit{Elliptic} dataset and \textit{HGCAE} scoring 80\% on \textit{Cora}. In contrast, Euclidean methods like \textit{DOMINANT} and \textit{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.
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In the era of digital transformation, the rapid increase in data complexity and volume has heightened the need for advanced anomaly detection techniques. Anomaly detection is essential across various domains, including cybersecurity, finance, and fraud detection, where it involves identifying unusual patterns that could indicate significant issues or potential threats. Traditional anomaly detection methods often fall short when dealing with the growing complexity and scale of modern data. Conventional techniques, like classification and clustering, are generally designed for tabular data and struggle with the intricacies of more complex structures. Graph-based anomaly detection has emerged as a promising approach due to its ability to model intricate relationships within data. By representing data as graphs, where nodes denote entities and edges represent their interactions, this method captures complex patterns that might be missed by traditional techniques [12]. Graph embeddings, which transform graph data into lower-dimensional vector spaces, further enhance anomaly detection by preserving the structural information and revealing subtle patterns indicative of anomalies [25]. A significant advancement in this field is the use of hyperbolic space for graph embeddings. Hyperbolic space, characterized by its constant negative curvature, provides a powerful framework for modeling hierarchical and complex relationships present in real-world data [11]. Unlike Euclidean space, which can distort hierarchical structures, hyperbolic space allows for more accurate representation of these relationships, leading to improved performance in anomaly detection tasks [63]. Existing surveys have provided valuable insights into various aspects of hyperbolic geometry in machine learning and graph-based methods, yet there remains a lack of comprehensive syntheses and algorithmic analyses of hyperbolic graph embedding techniques. For instance, [53] provides a general survey on hyperbolic deep neural networks (HDNNs), exploring their architectures and applications across diverse domains, while [78] focuses specifically on hyperbolic graph neural networks (HGNNs), unifying existing approaches into a general framework and summarizing their key components and applications. However, while these studies provide valuable context, None of these surveys have thoroughly examined the feasibility of these methods on a specific use case to establish a well-founded comparison. Moreover, none of them implement these methods for experimental benchmarking. In our survey, not only do we review and classify existing methods, but we also provide a library that implements the most significant approaches, along with a framework that allows for testing their effectiveness in the task of anomaly detection, a classification problem. By bridging this gap, our work offers both a theoretical synthesis and a practical evaluation, facilitating a more rigorous assessment of these methods in real-world applications. Our contributions include:
• Detailed Review and Analysis : We present a thorough review a of existing hyperbolic graph embedding techniques.
• Exploration on anomaly detection: We investigate the application of hyperbolic graph embeddings on anomaly detection, highlighting their advantages over traditional methods by evaluating them on established datasets.
The remainder of this paper is structured as follows: Section 2 provides the necessary background on graph embedding and highlighting the main methods in the Euclidean space. Section 3 introduces the hyperbolic space covering key concepts in differential geometry, and hyperbolic geometry graph and its key concepts. It also proposes a comprehensive taxonomy of hyperbolic graph embedding models, categorizing the existing techniques into traditional methods and deep learning-based methods. Section 4 outlines the methodology we followed for using hyperbolic embedding for the anomaly detection task. We also introduce the Ghypeddings library we constructed for this purpose. Section 5 describes the experimental setup, including datasets, evaluation metrics, and presents the experimental results, discussing the key findings. Finally, Section 6 concludes the paper and offers insights into potential future research directions.
In this section, we define the concepts of graphs and graph embedding. Then we present the commonly used techniques of graph embedding in the Euclidean space.
Graphs are powerful data structures used to model relationships among entities in various domains. However, their irregular structure presents challenges for conventional machine learning models designed to process tabular data. Graph embeddings address this issue by mapping graph data into a lowdimensional, continuous vector
