Bridging the Space Gap: Unifying Geometry Knowledge Graph Embedding with Optimal Transport

Knowledge Graph Embedding (KGE) is a critical field aiming to transform the elements of knowledge graphs (KGs) into continuous spaces, offering great potential for structured data representation. In contemporary KGE research, the utilization of either hyperbolic or Euclidean space for knowledge graph Embedding is a common practice. However, knowledge graphs encompass diverse geometric data structures, including chains and hierarchies, whose hybrid nature exceeds the capacity of a single embedding space to capture effectively. This paper introduces a novel and highly effective approach called Unified Geometry Knowledge Graph Embedding (UniGE) to address the challenge of representing diverse geometric data in KGs. UniGE stands out as a novel KGE method that seamlessly integrates KGE in both Euclidean and hyperbolic geometric spaces. We introduce an embedding alignment method and fusion strategy, which harnesses optimal transport techniques and the Wasserstein barycenter method. Furthermore, we offer a comprehensive theoretical analysis to substantiate the superiority of our approach, as evident from a more robust error bound. To substantiate the strength of UniGE, we conducted comprehensive experiments on three benchmark datasets. The results consistently demonstrate that UniGE outperforms state-of-the-art methods, aligning with the conclusions drawn from our theoretical analysis.