Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides theoretical analysis and empirical results on when and where to use hyperbolic space and hyperbolic embeddings in recommender systems. Specifically, we answer the questions that which type of models and datasets are more suited for hyperbolic space, as well as which latent size to choose. We evaluate our answers by comparing the performance of Euclidean space and hyperbolic space on different latent space models in both general item recommendation domain and social recommendation domain, with 6 widely used datasets and different latent sizes. Additionally, we propose a new metric learning based recommendation method called SCML and its hyperbolic version HSCML. We evaluate our conclusions regarding hyperbolic space on SCML and show the state-of-the-art performance of hyperbolic space by comparing HSCML with other baseline methods.

翻译：超曲空间和双曲嵌入器正在成为推荐人系统受欢迎的研究领域。 但是,不清楚在什么情况下应该考虑超曲空间。 为了填补这一空白,本文件提供了理论分析和实验结果,说明何时和何处在推荐人系统中使用双曲空间和双曲嵌入器。 具体地说,我们回答了哪些类型的模型和数据集更适合双曲空间,以及哪些潜伏大小可供选择的问题。 我们通过比较一般建议域和社会建议域的不同潜在空间模型,以及6个广泛使用的数据集和不同潜伏大小,来评估我们的答复。 此外,我们提出了一种新的基于建议的方法,即SCML及其双曲版HSCML。 我们通过将HSCML与其他基线方法进行比较,评估我们关于超曲空间的超曲空间的结论,并展示超曲空间的最新表现。