Knowledge Graph Completion via Complex Tensor Factorization

TL;DR

This paper introduces a novel complex-valued embedding method for knowledge graph completion that balances expressiveness and computational efficiency, outperforming existing models on standard benchmarks.

Contribution

It proposes a simple, scalable complex embedding approach based on Hermitian dot products, connecting complex matrix diagonalization with knowledge graph modeling.

Findings

Outperforms existing models on link prediction benchmarks

Remains linear in space and time complexity

Theoretically links complex embeddings to unitary diagonalization

Abstract

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation/adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.