ROLE: Rotated Lorentzian Graph Embedding Model for Asymmetric Proximity

Graph embedding, which aims to learn low-dimensional node representations to preserve original graph structures, has attracted extensive research interests. However, most existing graph embedding models represent nodes in Euclidean spaces, which cannot effectively preserve complex patterns, e.g., hierarchical structures. Very recently, several hyperbolic embedding models have been proposed to preserve the hierarchical information in negative curvature spaces. Nevertheless, existing hyperbolic models fail to model the asymmetric proximity between nodes. To address this, we investigate a new asymmetric hyperbolic network representation problem, which targets at jointly preserving the hierarchical structures and asymmetric proximity for general directed graphs. We solve this problem by proposing a novel Rotated Lorentzian Embedding (ROLE) model, which yields two main benefits. First, our model can effectively capture both implicit and explicit hierarchical structures that come from the network topology and category information of nodes, respectively. Second, it can model the asymmetric proximity using rotation transformations. Specifically, we represent each node with a Lorentzian embedding vector, and learn two rotation matrices to reflect the direction of edges. We conduct extensive experiments on four real-world directed graph datasets. Empirical results demonstrate that the proposed approach consistently outperforms various state-of-the-art embedding models. In particular, ROLE achieves HR@1 scores up to 19.8% higher and NDCG@5 scores up to 11.3% higher than the best baselines on the task of node recommendation