  Recently, Graph Convolution Network (GCN) based methods have achieved
outstanding performance for recommendation. These methods embed users and items
in Euclidean space, and perform graph convolution on user-item interaction
graphs. However, real-world datasets usually exhibit tree-like hierarchical
structures, which make Euclidean space less effective in capturing user-item
relationship. In contrast, hyperbolic space, as a continuous analogue of a
tree-graph, provides a promising alternative. In this paper, we propose a fully
hyperbolic GCN model for recommendation, where all operations are performed in
hyperbolic space. Utilizing the advantage of hyperbolic space, our method is
able to embed users/items with less distortion and capture user-item
interaction relationship more accurately. Extensive experiments on public
benchmark datasets show that our method outperforms both Euclidean and
hyperbolic counterparts and requires far lower embedding dimensionality to
achieve comparable performance.
