This thesis, authored by Zhou Haojie at the Cyprus University of Technology, presents a comprehensive comparative study of hyperbolic embedding methods applied to real-world networks, focusing on the intersection and contrast between machine learning approaches and traditional network science techniques. Hyperbolic embeddings have become a powerful tool for representing complex network data, enabling more efficient analysis of structural properties and facilitating downstream tasks such as link prediction, classification, and anomaly detection. The work is situated at the confluence of two rapidly evolving fields—machine learning and network science—each offering distinct methodologies for network representation and analysis.
Systematic Comparison: The thesis systematically compares state-of-the-art hyperbolic embedding methods from both machine learning and network science perspectives. It evaluates their performance on a variety of real-world networks, considering multiple downstream tasks such as mapping accuracy, greedy routing, and link prediction. This dual perspective allows for a nuanced understanding of the strengths and limitations inherent to each methodological tradition.
Evaluation Metrics: The study employs a range of quantitative metrics to assess embedding quality, including computational complexity, scalability, and sensitivity to network characteristics like degree distribution, modularity, and clustering coefficient. By doing so, it provides a holistic view of how different embedding strategies perform under diverse network conditions.
Integration of Approaches: The thesis explores the potential for integrating data-driven machine learning models with model-based network science methods. It highlights the flexibility of machine learning approaches, which do not rely on strong generative assumptions, and contrasts this with the interpretability and theoretical grounding of network science models. The work also discusses recent advances in embedding multilayer networks and the use of the Poincaré disk model for improved geometric representation and interpretability.
Practical Insights: Through extensive experimentation, the thesis identifies practical trade-offs between embedding accuracy, computational efficiency, and applicability to different types of networks. It offers guidance for practitioners on selecting appropriate embedding methods based on specific network properties and analytic goals.
This thesis makes a significant contribution to both the theoretical and practical understanding of hyperbolic network embeddings. By bridging the gap between machine learning and network science, it advances the state of the art in network representation learning and provides actionable insights for researchers and practitioners working with complex network data. The findings are particularly relevant for applications in social network analysis, biological network modeling, cybersecurity, and any domain where understanding the latent geometry of networked systems is crucial. The comparative framework and recommendations established in this work are poised to inform future research and development of more robust, scalable, and interpretable network embedding algorithms.