# Quaternion Collaborative Filtering for Recommendation

arXiv: https://arxiv.org/abs/1906.02594 · HTML: https://mlsanity.com/paper/1906.02594/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 8 of 8)

- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [DaisyRec 2.0: Benchmarking Recommendation for Rigorous Evaluation](https://mlsanity.com/paper/2206.10848/) (2022)
- [Learning Heterogeneous Temporal Patterns of User Preference for Timely Recommendation](https://mlsanity.com/paper/2104.14200/) (2021)
- [Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling](https://mlsanity.com/paper/2104.01716/) (2021)
- [Global Context Enhanced Social Recommendation with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2110.04039/) (2021)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [Fully tensorial approach to hypercomplex-valued neural networks](https://mlsanity.com/paper/2407.00449/) (2024)
- [An Effective, Robust and Fairness-aware Hate Speech Detection Framework](https://mlsanity.com/paper/2409.17191/) (2024)

## Abstract (arXiv)

This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias as compared with the real-space inner product. All in all, we conduct extensive experiments on six real-world datasets, demonstrating the effectiveness of Quaternion algebra in recommender systems. The results exhibit that QCF outperforms a wide spectrum of strong neural baselines on all datasets. Ablative experiments confirm the effectiveness of Hamilton-based composition over multi-embedding composition in real space.