Improving static and temporal knowledge graph embedding using affine transformations of entities

To find a suitable embedding for a knowledge graph (KG) remains a big challenge nowadays. By measuring the distance or plausibility of triples and quadruples in static and temporal knowledge graphs, many reliable knowledge graph embedding (KGE) models are proposed. However, these classical models may not be able to represent and infer various relation patterns well, such as TransE cannot represent symmetric relations, DistMult cannot represent inverse relations, RotatE cannot represent multiple relations, etc.. In this paper, we improve the ability of these models to represent various relation patterns by introducing the affine transformation framework. Specifically, we first utilize a set of affine transformations related to each relation or timestamp to operate on entity vectors, and then these transformed vectors can be applied not only to static KGE models, but also to temporal KGE models. The main advantage of using affine transformations is their good geometry properties with interpretability. Our experimental results demonstrate that the proposed intuitive design with affine transformations provides a statistically significant increase in performance with adding a few extra processing steps and keeping the same number of embedding parameters. Taking TransE as an example, we employ the scale transformation (the special case of an affine transformation). Surprisingly, it even outperforms RotatE to some extent on various datasets. We also introduce affine transformations into RotatE, Distmult, ComplEx, TTransE and TComplEx respectively, and experiments demonstrate that affine transformations consistently and significantly improve the performance of state-of-the-art KGE models on both static and temporal knowledge graph benchmarks.