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.

翻译：知识图谱嵌入的主要目标是学习实体和关系的低维表示，从而预测缺失事实。实现更优知识图谱嵌入的一个重要挑战在于捕捉关系模式，包括对称性、反对称性、逆关系、交换复合、非交换复合、层次性和多重性。本研究提出了一种名为3H-TH（双曲空间中的三维旋转与平移）的新模型，能够同时捕捉这些关系模式。相比之下，以往的尝试未能同时在所有上述属性上取得令人满意的性能。实验结果表明，新模型在低维空间中，在准确性、层次属性及其他关系模式方面优于现有最先进模型，同时在高维空间中表现相近。