  The cascade of 2D geometric transformations were exploited to model relations
between entities in a knowledge graph (KG), leading to an effective KG
embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was
proposed as a new KGE model, Rotate3D, by leveraging its non-commutative
property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric
transformations, including translation, rotation, scaling, reflection, and
shear and propose a family of KGE models, named CompoundE3D, in this work.
CompoundE3D allows multiple design variants to match rich underlying
characteristics of a KG. Since each variant has its own advantages on a subset
of relations, an ensemble of multiple variants can yield superior performance.
The effectiveness and flexibility of CompoundE3D are experimentally verified on
four popular link prediction datasets.
