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.
The original multilinear model is symmetric in subject and object for every relation @cite_1 and achieves good performance on FB15K and WN18 data sets. However it is likely due to the absence of true negatives in these data sets, as discussed in Section .
@cite_1
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Models that learn to represent textual and knowledge base relations in the same continuous latent space are able to perform joint inferences among the two kinds of relations and obtain high accuracy on knowledge base completion (, 2013). In this paper we propose a model that captures the compositional structure of textual relations, and jointly optimizes entity, knowledge base, and textual relation representations. The proposed model significantly improves performance over a model that does not share parameters among textual relations with common sub-structure.