Abstract: Most of existing knowledge graph completion methods often neglect the semantic hierarchical differences that objectively exist between entities. To address these limitations, we propose a knowledge graph completion method named spherical hierarchical knowledge completion (SpHKC), which models semantic hierarchical phenomena using spherical coordinates. In this method, entities are mapped to points on a spherical surface, and entities located on different spheres correspond to different semantic hierarchy levels. The radius of the sphere determines the level of the semantic hierarchy for entities on that sphere, with larger spheres representing lower levels. Relationships are modeled as movements from one entity on the spherical surface to another entity (on the same or different spheres), involving rotation and positioning operations to handle both similar and different semantic hierarchy levels between entities. The polar angle and azimuth angle in spherical coordinates provide entities with richer expressions. Experimental results demonstrate that SpHKC achieves comparable performance to state-of-the-art methods on the FB15k-237 and WN18RR datasets. Moreover, it consistently improves important metrics such as MRR (mean reciprocal ranking) and Hits@10 by approximately 1% compared to recent algorithms on the YAGO3-10 dataset, showcasing the effectiveness of incorporating semantic hierarchical information.

Key words: knowledge graph, knowledge graph completion, knowledge graph embedding, semantic hierarchical information, semantic hierarchy structure, spherical coordinate