  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.
