  The bilinear method is mainstream in Knowledge Graph Embedding (KGE), aiming
to learn low-dimensional representations for entities and relations in
Knowledge Graph (KG) and complete missing links. Most of the existing works are
to find patterns between relationships and effectively model them to accomplish
this task. Previous works have mainly discovered 6 important patterns like
non-commutativity. Although some bilinear methods succeed in modeling these
patterns, they neglect to handle 1-to-N, N-to-1, and N-to-N relations (or
complex relations) concurrently, which hurts their expressiveness. To this end,
we integrate scaling, the combination of translation and rotation that can
solve complex relations and patterns, respectively, where scaling is a
simplification of projection. Therefore, we propose a corresponding bilinear
model Scaling Translation and Rotation (STaR) consisting of the above two
parts. Besides, since translation cannot be incorporated into the bilinear
model directly, we introduce translation matrix as the equivalent. Theoretical
analysis proves that STaR is capable of modeling all patterns and handling
complex relations simultaneously, and experiments demonstrate its effectiveness
on commonly used benchmarks for link prediction.
