Hyperbolic geometric graph representation learning: A survey

Graph representation learning is a crucial technology, which converts graph data into low-dimensional vector representations and significantly enhances various machine learning tasks. Traditional Euclidean space often faces the curse of dimensionality when representing graph structures, especially for graph data possessing complex relationships. Hyperbolic geometry, as a form of non-Euclidean geometry, has superior capabilities to more accurately capture the graph data of nonlinear relationships and hierarchical structures, making it an effective tool for handling complex graph data. To stimulate future research, this paper presents a comprehensive reviews of literature around the graph representation learning in hyperbolic geometry. We offer a new taxonomy of hyperbolic graph representation methods by embedding graph data with different structures into various geometric spaces, including hyperbolic space graph representation learning and spatial fusion graph representation learning. Moreover, it emphasizes the applications of hyperbolic geometric representation learning across various domains, such as knowledge graphs, recommendation systems, biomolecular analysis, and natural language processing, while also exploring potential future research directions.