5* Knowledge Graph Embeddings with Projective Transformations

Performing link prediction using knowledge graph embedding (KGE) models is a popular approach for knowledge graph completion. Such link predictions are performed by measuring the likelihood of links in the graph via a transformation function that maps nodes via edges into a vector space. Since the complex structure of the real world is reflected in multi-relational knowledge graphs, the transformation functions need to be able to represent this complexity. However, most of the existing transformation functions in embedding models have been designed in Euclidean geometry and only cover one or two simple transformations. Therefore, they are prone to underfitting and limited in their ability to embed complex graph structures. The area of projective geometry, however, fully covers inversion, reflection, translation, rotation, and homothety transformations. We propose a novel KGE model, which supports those transformations and subsumes other state-of-the-art models. The model has several favorable theoretical properties and outperforms existing approaches on widely used link prediction benchmarks

Correspondences between projective planes

We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.Comment: Improved readability, 14 page