On the Equivalence of Holographic and Complex Embeddings for Link Prediction

TL;DR

This paper demonstrates that holographic embeddings and complex embeddings for link prediction are fundamentally equivalent, with spectral analysis revealing their close relationship and enabling conversions between the two methods.

Contribution

It establishes the theoretical equivalence between holographic and complex embeddings, providing insights into their relationship and potential for unified understanding.

Findings

Spectral version of holographic embedding analyzed using Fourier transform.

Holographic embedding can be viewed as a constrained form of complex embedding.

Any complex embedding can be converted into an equivalent holographic embedding.

Abstract

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.