Hybrid Interaction Temporal Knowledge Graph Embedding Based on Householder Transformations

Temporal Knowledge Graph Embedding (TKGE) is a crucial technique for performing Temporal Knowledge Graph Completion (TKGC). The effectiveness of TKGE largely depends on the ability to model intrinsic relation patterns. However, as we know, most existing TKGE models usually embed KGs into a single geometric space such as Euclidean, hyperbolic or hyperspherical space to maintain their specific geometric structures (e.g., chain, hierarchy, and ring structures). None of the existing methods can simultaneously model relation patterns of chain, hierarchy, ring structures, and relation mapping properties. This paper constructs a hybrid interaction TKGE model HyIE, which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. HyIE performs two Householder transformations of head and tail entities parameterized by relations in a high-dimensional mixed vector space. The curvature of hyperbolic and hyperspherical spaces depends on the product of both relation and temporal. The core of HyIE lies in implementing transformations and interactions of vectors in Euclidean, hyperbolic and hyperspherical spaces, and Household transformation of head and tail entities. Theoretically, HyIE can model crucial relation patterns and mapping properties simultaneously. Experimental results on five temporal knowledge graph benchmarks show that our HyIE achieves state-of-the-art performance.