Affine Transformation-Based Knowledge Graph Embedding

Real-world knowledge graphs are often incomplete. The challenge in knowledge graph completion primarily stems from complex relations and various relation patterns within the knowledge graph (KG). Traditional geometric translation methods in Knowledge Graph Embedding (KGE) commonly treat relations as geometric transformation operations on entities, such as rotation, translation, and scaling-operations frequently used in image processing. Note that affine transformation is also a common operation in image processing, and compared with those models using a single geometric operation, affine transformation can better capture the intrinsic semantics nested in the KG. Therefore, we propose a KGE method based on affine transformations, named Affine Transformation Embedding (ATE). We consider relations as a form of affine transformation, calculating the distance between head and tail entities after the relation transformation. Theoretically, we have proved that ATE can effectively model complex relations and encode various relation patterns. Experimentally, we have tested four datasets for the link prediction task, and the empirical results demonstrate that, for the link prediction task, ATE achieves better performance than existing SOTA baselines.