User-item interaction data in collaborative filtering and graph modeling tasks often exhibit power-law characteristics, which suggest the suitability of hyperbolic space modeling. Hyperbolic Graph Convolution Neural Networks (HGCNs) are a novel technique that leverages the advantages of GCN and hyperbolic space, and then achieves remarkable results. However, existing HGCN methods have several drawbacks: they fail to fully leverage hyperbolic space properties due to arbitrary embedding initialization and imprecise tangent space aggregation; they overlook auxiliary information that could enrich the collaborative graph; and their training convergence is slow due to margin ranking loss and random negative sampling. To overcome these challenges, we propose Hyperbolic Graph Collaborative for Heterogeneous Recommendation (HGCH), an enhanced HGCN-based model for collaborative filtering that integrates diverse side information into a heterogeneous collaborative graph and improves training convergence speed. HGCH first preserves the long-tailed nature of the graph by initializing node embeddings with power law prior; then it aggregates neighbors in hyperbolic space using the gyromidpoint method for accurate computation; finally, it fuses multiple embeddings from different hyperbolic spaces by the gate fusion with prior. Moreover, HGCH employs a hyperbolic user-specific negative sampling to speed up convergence. We evaluate HGCH on four real datasets, and the results show that HGCH achieves competitive results and outperforms leading baselines, including HGCNs. Extensive ablation studies further confirm its effectiveness.

翻译：协同过滤与图建模任务中的用户-物品交互数据常呈现幂律分布特征，这暗示了采用双曲空间建模的适用性。双曲图卷积神经网络（HGCNs）是一种融合GCN与双曲空间优势的新兴技术，已取得显著成果。然而，现有HGCN方法存在若干缺陷：由于任意嵌入初始化和不精确的切空间聚合，未能充分利用双曲空间特性；忽略了可丰富协同图的辅助信息；且因边际排序损失和随机负采样导致训练收敛缓慢。为克服这些挑战，我们提出面向异构推荐的双曲图协同模型（HGCH），这是一种基于HGCN的增强型协同过滤模型，可将多元辅助信息整合至异构协同图中并提升训练收敛速度。HGCH首先通过幂律先验初始化节点嵌入以保持图结构的长尾特性；继而采用陀螺中点法在双曲空间中进行邻域聚合以实现精确计算；最后通过带先验的门控融合机制整合来自不同双曲空间的多元嵌入。此外，HGCH采用双曲用户特定负采样策略以加速收敛。我们在四个真实数据集上评估HGCH，结果表明其取得了具有竞争力的优异性能，并超越了包括HGCNs在内的主流基线模型。大量消融实验进一步验证了其有效性。