Hyperbolic Node Structural Role Embedding

Hyperbolic space has been shown to be able to naturally reflect the properties of complex networks that exhibit hierarchical structure. This has led to the development of a number of hyperbolic network representation learning methods which have been shown to be on average superior to the more traditional network representation learning in Euclidean space. The main focus of existing hyperbolic network embedding methods has been local (i.e., microscopic) node embedding. That is, learning node embeddings based on their local neighborhood. Work on hyperbolic network embedding has so far not investigated hyperbolic node structural role embedding (i.e., macroscopic embedding). That is, learning node embeddings based on their structural roles.In this work, we attempt to address this gap by extending two commonly used methods used for Euclidean structural role embedding–Random walk and Matrix factorization–to perform structural role embedding in hyperbolic space. Specifically, we show how Euclidean structural role embeddings methods utilizing these methods can be moved into hyperbolic space. Experiments on several real-world and synthetic networks show that our structural role embedding methods in hyperbolic space achieve better results than their Euclidean counterparts, with one of our methods outperforming the current state-of-the-art. Our results add further support to the growing body of literature that show that hyperbolic space is more effective than Euclidean space for graph representation learning, specifically in our case, node structural role representations.