Block-Diagonal Orthogonal Relation and Matrix Entity for Knowledge Graph
  Embedding
Yihua Zhu Hidetoshi Shimodaira
The primary aim of Knowledge Graph embeddings (KGE) is to learn
low-dimensional representations of entities and relations for predicting
missing facts. While rotation-based methods like RotatE and QuatE perform well
in KGE, they face two challenges: limited model flexibility requiring
proportional increases in relation size with entity dimension, and difficulties
in generalizing the model for higher-dimensional rotations. To address these
issues, we introduce OrthogonalE, a novel KGE model employing matrices for
entities and block-diagonal orthogonal matrices with Riemannian optimization
for relations. This approach enhances the generality and flexibility of KGE
models. The experimental results indicate that our new KGE model, OrthogonalE,
is both general and flexible, significantly outperforming state-of-the-art KGE
models while substantially reducing the number of relation parameters.