On the Equivalence of Holographic and Complex Embeddings for Link Prediction

Understand

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.