Embedding Hierarchical Tree Structure of Concepts in Knowledge Graph Embedding

Knowledge Graph Embedding aims to encode both entities and relations into a continuous low-dimensional vector space, which is crucial for knowledge-driven application scenarios. As abstract entities in knowledge graphs, concepts inherently possess unique hierarchical structures and encompass rich semantic information. Although existing methods for jointly embedding concepts and instances achieve promising performance, they still face two issues: (1) They fail to explicitly reconstruct the hierarchical tree structure of concepts in the embedding space; (2) They ignore disjoint concept pairs and overlapping concept pairs derived from concepts. In this paper, we propose a novel concept representation approach, called Hyper Spherical Cone Concept Embedding (HCCE), to explicitly model the hierarchical tree structure of concepts in the embedding space. Specifically, HCCE represents each concept as a hyperspherical cone and each instance as a vector, maintaining the anisotropy of concept embeddings. We propose two variant methods to explore the impact of embedding concepts and instances in the same or different spaces. Moreover, we design score functions for disjoint concept pairs and overlapping concept pairs, using relative position relations to incorporate them seamlessly into our geometric models. Experimental results on three benchmark datasets show that HCCE outperforms most existing state-of-the-art methods on concept-related triples and achieves competitive results on instance-related triples. The visualization of embedding results intuitively shows the hierarchical tree structure of concepts in the embedding space.