The main objective of Knowledge Graph (KG) embeddings is to learn low-dimensional representations of entities and relations, enabling the prediction of missing facts. A significant challenge in achieving better KG embeddings lies in capturing relation patterns, including symmetry, antisymmetry, inversion, commutative composition, non-commutative composition, hierarchy, and multiplicity. This study introduces a novel model called 3H-TH (3D Rotation and Translation in Hyperbolic space) that captures these relation patterns simultaneously. In contrast, previous attempts have not achieved satisfactory performance across all the mentioned properties at the same time. The experimental results demonstrate that the new model outperforms existing state-of-the-art models in terms of accuracy, hierarchy property, and other relation patterns in low-dimensional space, meanwhile performing similarly in high-dimensional space.

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