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.

翻译：推荐任务中用户-物品交互数据天然具有幂律分布特性，近期协同过滤方法开始引入双曲空间建模。其中，双曲图卷积网络（Hyperbolic GCN）融合了图卷积网络与双曲空间的优势，取得了令人瞩目的性能。然而，由于完全随机的嵌入初始化与不精确的切空间聚合机制，现有方法仅部分利用了双曲空间的特性。此外，这些工作主要聚焦于用户-物品交互数据，进一步限制了模型性能。本文提出双曲图卷积协同过滤模型HGCC，该模型改进了现有面向协同过滤的双曲图卷积结构并整合了辅助信息：首先通过为节点嵌入初始化添加幂律先验，保留协同图的长尾分布特性；随后利用陀螺中点方法直接在多个双曲空间中进行邻居聚合，以获得更精确的计算结果；最后通过带先验的门控融合机制，自动融合同一节点在不同双曲空间中的多重嵌入。在四个真实数据集上的实验表明，我们的模型具有强竞争力，其性能超越包括双曲图卷积网络在内的主流基线方法。进一步实验验证了所提方法的有效性，并通过学习到的嵌入给出了深入解释。