Abstract

The aim of Knowledge Graph Embedding (KGE) is to acquire low-dimensional representations of entities and relationships for the purpose of predicting new valid triples, thereby enhancing the functionality of intelligent networks that rely on accurate data representation.In recommendation systems, for example, the model can enhance personalized suggestions by better understanding user-item relationships, especially when the relationships are hierarchical, such as in the case of user preferences across different product categories. Existing KGE models mostly learn embeddings in Euclidean space, which perform well in high-dimensional settings. However, in low-dimensional scenarios, these models struggle to accurately capture the hierarchical information of relationships in knowledge graphs (KG), a limitation that can adversely affect the performance of intelligent network systems where structured knowledge is critical for decision making and operational efficiency. Recently, the MuRP model was proposed, introducing the use of hyperbolic space for KG embedding. Using the properties of hyperbolic space, where the space near the center is small and the space away from the center is large, the MuRP model achieves effective KG embedding even in low-dimensional training conditions, making it particularly suitable for dynamic environments typical of intelligent networks. Therefore, this paper proposes a method that utilizes the characteristics of hyperbolic geometry to create an embedding model in hyperbolic space, combining translation and multi-dimensional rotation geometric transformations. This model accurately represents various relationship patterns in knowledge graphs, including symmetry, asymmetry, inversion, composition, hierarchy, and multiplicity, which are essential for enabling robust interactions in intelligent network frameworks. Experimental results demonstrate that the proposed model generally outperforms Euclidean space embedding models under low-dimensional training conditions and performs comparably to other hyperbolic KGE models. In experiments using the WN18RR dataset, the Hits@10 metric improved by 0.3% compared to the baseline model, and in experiments using the FB15k-237 dataset, the Hits@3 metric improved by 0.1% compared to the baseline model, validating the reliability of the proposed model and its potential contribution to advancing intelligent network applications.