Knowledge graph representation via hierarchical hyperbolic neural graph embedding

Knowledge graph enhanced information retrieval systems have attracted considerable attention due to their ability to improve performance and provide additional explainability. As the knowledge graphs usually include fruitful facts, they are also good sources of side information. However, recent studies have shown that the usefulness of knowledge graphs depends highly on their representation, e.g., the embeddings of entities and relations. Embedding entities and relations in low-dimensional space is a successful knowledge graph representation solution. Most of the works lie in modeling symmetry/asymmetry/composition/inversion relations but pay less attention to the hierarchical relations. Recent studies have observed the fact that there exist rich semantic hierarchical relations in knowledge graphs such as Freebase (entities are connected in a taxonomic hierarchy) and WordNet (entities are synsets linked together in a hierarchy).

To address the above problems, we propose Hierarchical Hyperbolic Neural Graph Embedding (H2E), a new knowledge graph representation approach, which is able to better preserve hierarchical relations. Specifically, the entities/relations representations are learned in a hyperbolic polar embedding space. In a hyperbolic polar embedding space, the entity and relation are modeled as a dual-embedding with modulus embedding part and phase embedding part, enabling the explicitly modeling of two types of hierarchies: inter-level hierarchy and intra-level hierarchy. As the polar embedding is defined in hyperbolic space, the ability of modeling and inferring hierarchical relations are mutual enhanced. In addition, by noticing the existence of the rich relational context, we propose an attentional neural context aggregation to adaptively integrate the relational context for further enhancing the ability to preserve the hierarchical relations. The empirical study on three benchmark datasets for the link prediction task demonstrates significant performance gains compared to some existing state-of-the-art methods and verifies the effectiveness of the proposed method on hierarchical relations.