5* Knowledge Graph Embeddings with Projective Transformations

TL;DR

This paper introduces a novel knowledge graph embedding model in projective geometry that supports multiple transformations simultaneously, improving link prediction performance on standard benchmarks.

Contribution

The proposed 5*E model is the first to support multiple transformations in projective geometry for knowledge graph embeddings, capturing complex subgraph structures.

Findings

Outperforms existing models on link prediction benchmarks

Supports multiple transformations like inversion, reflection, translation, rotation, and homothety

Has favorable theoretical properties

Abstract

Performing link prediction using knowledge graph embedding models has become a popular approach for knowledge graph completion. Such models employ a transformation function that maps nodes via edges into a vector space in order to measure the likelihood of the links. While mapping the individual nodes, the structure of subgraphs is also transformed. Most of the embedding models designed in Euclidean geometry usually support a single transformation type - often translation or rotation, which is suitable for learning on graphs with small differences in neighboring subgraphs. However, multi-relational knowledge graphs often include multiple sub-graph structures in a neighborhood (e.g. combinations of path and loop structures), which current embedding models do not capture well. To tackle this problem, we propose a novel KGE model (5*E) in projective geometry, which supports multiple simultaneous transformations - specifically inversion, reflection, translation, rotation, and homothety. The model has several favorable theoretical properties and subsumes the existing approaches. It outperforms them on the most widely used link prediction benchmarks