  Knowledge graph embedding (KGE) has been shown to be a powerful tool for
predicting missing links of a knowledge graph. However, existing methods mainly
focus on modeling relation patterns, while simply embed entities to vector
spaces, such as real field, complex field and quaternion space. To model the
embedding space from a more rigorous and theoretical perspective, we propose a
novel general group theory-based embedding framework for rotation-based models,
in which both entities and relations are embedded as group elements.
Furthermore, in order to explore more available KGE models, we utilize a more
generic group structure, module, a generalization notion of vector space.
Specifically, under our framework, we introduce a more generic embedding
method, ModulE, which projects entities to a module. Following the method of
ModulE, we build three instantiating models: ModulE$_{\mathbb{R},\mathbb{C}}$,
ModulE$_{\mathbb{R},\mathbb{H}}$ and ModulE$_{\mathbb{H},\mathbb{H}}$, by
adopting different module structures. Experimental results show that
ModulE$_{\mathbb{H},\mathbb{H}}$ which embeds entities to a module over
non-commutative ring, achieves state-of-the-art performance on multiple
benchmark datasets.
