Hypercomplex Graph Collaborative Filtering

Anchen Li, Bo Yang, Huan Huo, Farookh Khadeer Hussain

Abstract: Hypercomplex algebras are well-developed in the area of mathematics. Recently, several hypercomplex recommendation approaches have been proposed and yielded great success. However, two vital issues have not been well-considered in existing hypercomplex recommenders. First, these methods are only designed for specific and low-dimensional hypercomplex algebras (e.g., complex and quaternion algebras), ignoring the exploration and utilization of high-dimensional ones. Second, most recommenders treat every user-item interaction as an isolated data instance, without considering high-order collaborative relationships. To bridge these gaps, in this paper, we propose a novel recommendation framework named HyperComplex Graph Collaborative Filtering (HCGCF). To study the high-dimensional hypercomplex algebras, we introduce Cayley–Dickson construction which utilizes a recursive process to define hypercomplex algebras and their mathematical operations. Based on Cayley–Dickson construction, we devise a hypercomplex graph convolution operator to learn user and item representations. Specifically, the operator models both the neighborhood summary and interaction relations with neighbors in hypercomplex spaces, effectively exploiting the high-order connectivity in the user-item bipartite graph. To the best of our knowledge, it is the first time that Cayley-Dickson construction and graph convolution techniques have been explicitly discussed and used in hypercomplex recommender systems. Compared with several state-of-the-art recommender baselines, HCGCF achieves superior performance in both click-through rate prediction and top-K recommendation on three real-world datasets.