In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
A recent novel way to handle antisymmetry is via the Holographic Embeddings (HolE) model by @cite_3 . In HolE the circular correlation is used for combining entity embeddings, measuring the covariance between embeddings at different dimension shifts. This generally suggests that other composition functions than the classical tensor product can be helpful as they allow for a richer interaction of embeddings. However, the asymmetry in the composition function in HolE stems from the asymmetry of circular correlation, an @math operation, whereas ours is inherited from the complex inner product, in @math .
@cite_3
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Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HOLE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator, HOLE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. Experimentally, we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction on knowledge graphs and relational learning benchmark datasets.