# On the Equivalence of Holographic and Complex Embeddings for Link Prediction

arXiv: https://arxiv.org/abs/1702.05563 · HTML: https://mlsanity.com/paper/1702.05563/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2017.

## Built on by (most cited first, 13 of 13)

- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [Relation-aware Graph Attention Model With Adaptive Self-adversarial Training](https://mlsanity.com/paper/2102.07186/) (2021)
- [Bilinear Scoring Function Search for Knowledge Graph Learning](https://mlsanity.com/paper/2107.00184/) (2021)
- [Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding](https://mlsanity.com/paper/2110.03789/) (2021)
- [Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform](https://mlsanity.com/paper/2211.03635/) (2022)
- [Prediction of Adverse Biological Effects of Chemicals Using Knowledge Graph Embeddings](https://mlsanity.com/paper/2112.04605/) (2021)
- [Multi-label Learning with Random Circular Vectors](https://mlsanity.com/paper/2407.05656/) (2024)
- [Unstructured Text Enhanced Open-domain Dialogue System: A Systematic Survey](https://mlsanity.com/paper/2411.09166/) (2024)
- [Learning Decorrelated Representations Efficiently Using Fast Fourier Transform](https://mlsanity.com/paper/2301.01569/) (2023)
- [Location Sensitive Embedding for Knowledge Graph Reasoning](https://mlsanity.com/paper/2401.10893/) (2023)
- [Sharing Parameter by Conjugation for Knowledge Graph Embeddings in Complex Space](https://mlsanity.com/paper/2404.11809/) (2024)
- [On The Expressive Power of Knowledge Graph Embedding Methods](https://mlsanity.com/paper/2407.16326/) (2024)

## Abstract (arXiv)

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.