Hyperbolic Graph Neural Networks: A Review of Methods and Applications

Graphs are data structures that extensively exist in real-world complex systems, varying from social networks [15, 62], protein interaction networks [52], recommender systems [9, 65, 64], knowledge graphs [56], to the financial transaction systems [40]. They form the basis of innumerable systems owing to their widespread utilization, allowing relational knowledge about interacting entities to be stored and accessible rapidly. Consequently, graph-related learning tasks gain increasing attention in machine learning and network science research. Many researchers have applied Graph Neural Networks (GNNs) for a variety of tasks, including node classification [23, 53, 59], link prediction [22, 71], and graph classification [61, 11] by embedding nodes in low-dimensional vector spaces, encoding topological and semantic information simultaneously. Many GNNs are built in Euclidean space in that it feature a vectorial structure, closed-form distance and inner-product formulae and is a natural extension of our intuitively appealing visual three-dimensional space [14]. Despite the effectiveness of Euclidean space for graph-related learning tasks, its ability to encode complex patterns is intrinsically limited by its polynomially expanding capacity. Although nonlinear techniques [3] assist in mitigating this issue, complex graph patterns may still need an embedding dimensionality that is computationally intractable. As revealed by recent research [4] many complex data show non-Euclidean underlying anatomy. For example, the tree-like structure extensively exists in many real-world networks, such as the hypernym structure in natural languages, the subordinate structure of entities in the knowledge graph, the organizational structure for financial fraud, and the power-law distribution in recommender systems.