  Due to the naturally power-law distributed nature of user-item interaction
data in recommendation tasks, hyperbolic space modeling has recently been
introduced into collaborative filtering methods. Among them, hyperbolic GCN
combines the advantages of GCN and hyperbolic space and achieves a surprising
performance. However, these methods only partially exploit the nature of
hyperbolic space in their designs due to completely random embedding
initialization and an inaccurate tangent space aggregation. In addition, the
data used in these works mainly focus on user-item interaction data only, which
further limits the performance of the models. In this paper, we propose a
hyperbolic GCN collaborative filtering model, HGCC, which improves the existing
hyperbolic GCN structure for collaborative filtering and incorporates side
information. It keeps the long-tailed nature of the collaborative graph by
adding power law prior to node embedding initialization; then, it aggregates
neighbors directly in multiple hyperbolic spaces through the gyromidpoint
method to obtain more accurate computation results; finally, the gate fusion
with prior is used to fuse multiple embeddings of one node from different
hyperbolic space automatically. Experimental results on four real datasets show
that our model is highly competitive and outperforms leading baselines,
including hyperbolic GCNs. Further experiments validate the efficacy of our
proposed approach and give a further explanation by the learned embedding.
