Modeling Noncommutative Composition of Relations for Knowledge Graph Embedding

Abstract

Knowledge Graph Embedding (KGE) is a powerful way to express Knowledge Graphs (KGs), which can help machines learn patterns hidden in the KGs. Relation patterns are useful hidden patterns, and they usually assist machines to predict unseen facts. Many existing KGE approaches can model some common relation patterns like symmetry/antisymmetry, inversion, and commutative composition patterns. However, most of them are weak in modeling noncommutative composition patterns. It means these approaches can not distinguish a lot of composite relations like “father’s mother” and “mother’s father”. In this work, we propose a new KGE method called QuatRotatScalE (QRSE) to overcome this weakness, since it utilizes rotation and scaling transformations of quaternions to design the relation embedding. Specifically, we embed the relations and entities into a quaternion vector space under the difference norm KGE framework. Since the multiplication of quaternions does not satisfy the commutative law, QRSE can model noncommutative composition patterns naturally. The experimental results on the synthetic dataset also support that QRSE has this ability. In addition, the experimental results on real-world datasets show that QRSE reaches state-of-the-art in link prediction problem.