  Knowledge graph is a popular format for representing knowledge, with many
applications to semantic search engines, question-answering systems, and
recommender systems. Real-world knowledge graphs are usually incomplete, so
knowledge graph embedding methods, such as Canonical decomposition/Parallel
factorization (CP), DistMult, and ComplEx, have been proposed to address this
issue. These methods represent entities and relations as embedding vectors in
semantic space and predict the links between them. The embedding vectors
themselves contain rich semantic information and can be used in other
applications such as data analysis. However, mechanisms in these models and the
embedding vectors themselves vary greatly, making it difficult to understand
and compare them. Given this lack of understanding, we risk using them
ineffectively or incorrectly, particularly for complicated models, such as CP,
with two role-based embedding vectors, or the state-of-the-art ComplEx model,
with complex-valued embedding vectors. In this paper, we propose a
multi-embedding interaction mechanism as a new approach to uniting and
generalizing these models. We derive them theoretically via this mechanism and
provide empirical analyses and comparisons between them. We also propose a new
multi-embedding model based on quaternion algebra and show that it achieves
promising results using popular benchmarks. Source code is available on GitHub
at https://github.com/tranhungnghiep/AnalyzeKGE.
