  Translation, rotation, and scaling are three commonly used geometric
manipulation operations in image processing. Besides, some of them are
successfully used in developing effective knowledge graph embedding (KGE)
models such as TransE and RotatE. Inspired by the synergy, we propose a new KGE
model by leveraging all three operations in this work. Since translation,
rotation, and scaling operations are cascaded to form a compound one, the new
model is named CompoundE. By casting CompoundE in the framework of group
theory, we show that quite a few scoring-function-based KGE models are special
cases of CompoundE. CompoundE extends the simple distance-based relation to
relation-dependent compound operations on head and/or tail entities. To
demonstrate the effectiveness of CompoundE, we conduct experiments on three
popular KG completion datasets. Experimental results show that CompoundE
consistently achieves the state of-the-art performance.
