Graph neural network for recommendation in complex and quaternion spaces

With the development of graph neural network, researchers begin to use bipartite graph to model user-item interactions for recommendation. It is worth noting that most of graph recommendation models represent users and items in the real-valued space, which ignore the rich representational capacity of the non-real space. Besides, the simplicity and symmetry of the inner product make it ineffectively capture the intricate antisymmetric relations between users and items in interaction modeling. In this paper, based on the framework of graph neural network, we propose Graph Collaborative Filtering for recommendation in Complex and Quaternion space (GCFC and GCFQ respectively). Specifically, we first use complex embeddings or quaternion embeddings to initialize users and items. Then, the Hermitian product (for GCFC) or Hamilton product (for GCFQ) and embedding propagation layers are used to further enrich the embeddings of users and items. As such, we can obtain both latent inter-dependencies and intra-dependencies between components of users and items. Finally, we aggregate the embeddings of different propagation layers and use the Hermitian or Hamilton product with inner product to obtain the intricate antisymmetric relations between users and items. We have carried out extensive experiments on four real-world datasets to verify the effectiveness of GCFC and GCFQ.