Knowledge graph embedding with the special orthogonal group in quaternion space for link prediction

Abstract

Graph embedding is an important technique for improving the quality of link prediction models on knowledge graphs. Although embedding based on neural networks can capture latent features with high expressive power, geometric embedding has other advantages, such as intuitiveness, interpretability, and few parameters. Several recent works have used rotation in quaternion space to enhance performance, yet these rotations have been limited to 3D representations. This paper proposes Rotate4D, a novel model that performs 4D rotations in quaternion space using a special orthogonal group. Specifically, Rotate4D begins by embedding entities in quaternion space, then rotates the head embedding to the tail embedding in two different ways (isoclinic and double rotation). The group structure helps decompose the relation into unit vectors to perform 4D rotations in quaternion space. In addition, quaternion scaling is applied to solve hierarchical relations. With this approach, the proposed model improved link prediction performance compared with state-of-the-art models on standard datasets, especially for the Hits@1 metric (an improvement of 2.72% to 3.49%). In addition to these experiments, we also theoretically prove that Rotate4D can model all relational patterns, including symmetry, anti-symmetry, inversion, and composition.