On the Equivalence of Holographic and Complex Embeddings for Link Prediction

We show the equivalence of two state-of-the-art models for link prediction/knowledge graph completion: Nickel et al's holographic embeddings and Trouillon et al.'s complex embeddings. We first consider a spectral version of the holographic embeddings, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting model reveals that it can be viewed as an instance of the complex embeddings with a certain constraint imposed on the initial vectors upon training. Conversely, any set of complex embeddings can be converted to a set of equivalent holographic embeddings.