  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.
