  Knowledge graph completion is an important task that aims to predict the
missing relational link between entities. Knowledge graph embedding methods
perform this task by representing entities and relations as embedding vectors
and modeling their interactions to compute the matching score of each triple.
Previous work has usually treated each embedding as a whole and has modeled the
interactions between these whole embeddings, potentially making the model
excessively expensive or requiring specially designed interaction mechanisms.
In this work, we propose the multi-partition embedding interaction (MEI) model
with block term format to systematically address this problem. MEI divides each
embedding into a multi-partition vector to efficiently restrict the
interactions. Each local interaction is modeled with the Tucker tensor format
and the full interaction is modeled with the block term tensor format, enabling
MEI to control the trade-off between expressiveness and computational cost,
learn the interaction mechanisms from data automatically, and achieve
state-of-the-art performance on the link prediction task. In addition, we
theoretically study the parameter efficiency problem and derive a simple
empirically verified criterion for optimal parameter trade-off. We also apply
the framework of MEI to provide a new generalized explanation for several
specially designed interaction mechanisms in previous models. The source code
is released at https://github.com/tranhungnghiep/MEI-KGE.
