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.

本文提供了关于在推荐系统中应该在什么情况下使用超半径空间和超半径嵌入的理论分析和实证结果，包括何种类型的模型和数据集更适合于超半径空间，以及选择哪个潜在空间大小，同时提出了一种名为 SCML 和其超半径版本 HSCML 的新的基于度量学习的推荐方法，并在不同的潜在空间模型中，包括通用项目推荐领域和社交推荐领域，以及 6 个广泛使用的数据集和不同的潜在空间大小上比较欧几里得空间和超半径空间的性能，通过将 HSCML 与其他基线方法进行比较，展示了超半径空间的最新性能。