On the Equivalence of Holographic and Complex Embeddings for Link Prediction
This clarifies the theoretical relationship between two state-of-the-art methods, which is incremental but important for researchers in knowledge graph completion.
The paper demonstrates that holographic and complex embeddings are equivalent for link prediction in knowledge graphs, showing each can be converted into the other without loss of performance.
We show the equivalence of two state-of-the-art link prediction/knowledge graph completion methods: Nickel et al's holographic embedding and Trouillon et al.'s complex embedding. We first consider a spectral version of the holographic embedding, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting method reveals that it can be viewed as an instance of the complex embedding with certain constraints cast on the initial vectors upon training. Conversely, any complex embedding can be converted to an equivalent holographic embedding.