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.