Knowledge Graph Embedding with 3D Compound Geometric Transformations

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. Inspired by the recent trend in KGE designs that leverage multiple transformation from SO(3) instead of SE(2), 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. We propose a beam search-based algorithm to locate the near-optimal embedding scoring function designs for different datasets in the vast search space resulted from different combinations of operator components. 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.