NagE: Non-Abelian Group Embedding for Knowledge Graphs

Abstract

We demonstrated the existence of a group algebraic structure hidden in relational knowledge embedding problems, which suggests that a group-based embedding framework is essential for designing embedding models. Our theoretical analysis explores merely the intrinsic property of the embedding problem itself hence is model independent. Motivated by the theoretical analysis, we have proposed a group theory-based knowledge graph embedding framework, in which relations are embedded as group elements, and entities are represented by vectors in group action spaces. We provide a generic recipe to construct embedding models associated with two instantiating examples: SO3E and SU2E, both of which apply a continuous non-Abelian group as the relation embedding. Empirical experiments using these two exampling models have shown state-of-the-art results on benchmark datasets.