In this work, we move beyond the traditional complex-valued representations,
introducing more expressive hypercomplex representations to model entities and
relations for knowledge graph embeddings. More specifically, quaternion
embeddings, hypercomplex-valued embeddings with three imaginary components, are
utilized to represent entities. Relations are modelled as rotations in the
quaternion space. The advantages of the proposed approach are: (1) Latent
inter-dependencies (between all components) are aptly captured with Hamilton
product, encouraging a more compact interaction between entities and relations;
(2) Quaternions enable expressive rotation in four-dimensional space and have
more degree of freedom than rotation in complex plane; (3) The proposed
framework is a generalization of ComplEx on hypercomplex space while offering
better geometrical interpretations, concurrently satisfying the key desiderata
of relational representation learning (i.e., modeling symmetry, anti-symmetry
and inversion). Experimental results demonstrate that our method achieves
state-of-the-art performance on four well-established knowledge graph
completion benchmarks.

本研究提出了一种基于超复数表示的知识图谱嵌入方法，利用四元数来表示实体并将关系建模为四维空间中的旋转方式，实验证明此方法在关系表示学习方面表现出色并达到了当前领域最好的水平。