Abstract
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