Hierarchy-Aware Quaternion Embedding for Knowledge Graph Completion

Knowledge graph completion is an essential task in the fields of graph mining and graph machine learning. Most contemporary approaches rely on geometric transformation to achieve knowledge graph completion, as geometry offers a well-defined mathematical foundation. For example, rotation transformations in rigid body transformation are frequently employed within quaternion spaces to model complex relation types in knowledge graphs. However, these models cannot effectively handle the hierarchical structure in the knowledge graph. As a result, the performance of knowledge graph completion suffers. To address this shortcoming of quaternion space, we propose a novel model that integrates hyperbolic space. Specifically, we perform a translation transformation in a hyperbolic space to obtain support vector embeddings that imply relation embedding. We then perform a rotation transformation with the Hamilton product in tangent space, treating the relation embedding as a rotation from the head entity embedding to the tail entity embedding. We verify the validity and generalization ability of our model on standard benchmark datasets including WN18RR, FB15k-237 and YAGO3-10. The experimental results show that our model achieves competitive results on MRR and H@K metrics. Our code is publicly available at https://github.com/llqy123/HAQE-master.