Cross-Domain Recommendation (CDR) seeks to utilize knowledge from different domains to alleviate the problem of data sparsity in the target recommendation domain, and it has been gaining more attention in recent years. Although there have been notable advancements in this area, most current methods represent users and items in Euclidean space, which is not ideal for handling long-tail distributed data in recommendation systems. Additionally, adding data from other domains can worsen the long-tail characteristics of the entire dataset, making it harder to train CDR models effectively. Recent studies have shown that hyperbolic methods are particularly suitable for modeling long-tail distributions, which has led us to explore hyperbolic representations for users and items in CDR scenarios. However, due to the distinct characteristics of the different domains, applying hyperbolic representation learning to CDR tasks is quite challenging. In this paper, we introduce a new framework called Hyperbolic Contrastive Learning (HCTS), designed to capture the unique features of each domain while enabling efficient knowledge transfer between domains. We achieve this by embedding users and items from each domain separately and mapping them onto distinct hyperbolic manifolds with adjustable curvatures for prediction. To improve the representations of users and items in the target domain, we develop a hyperbolic contrastive learning module for knowledge transfer. Extensive experiments on real-world datasets demonstrate that hyperbolic manifolds are a promising alternative to Euclidean space for CDR tasks.

翻译：跨域推荐旨在利用不同领域的知识来缓解目标推荐领域的数据稀疏问题，近年来受到越来越多的关注。尽管该领域已取得显著进展，但现有方法大多在欧几里得空间中表示用户和物品，这不适用于处理推荐系统中的长尾分布数据。此外，引入其他领域的数据可能加剧整个数据集的长尾特性，从而增加跨域推荐模型的有效训练难度。最新研究表明双曲几何方法特别适用于建模长尾分布，这促使我们探索在跨域推荐场景中使用双曲空间表示用户和物品。然而，由于不同领域具有各自独特的特征，将双曲表示学习应用于跨域推荐任务面临巨大挑战。本文提出名为双曲对比学习的新框架，该框架能够捕捉各领域的独有特征，同时实现领域间的高效知识迁移。我们通过分别嵌入每个领域的用户和物品，并将其映射到具有可调节曲率的独立双曲流形上进行预测。为提升目标领域用户和物品的表示质量，我们开发了用于知识迁移的双曲对比学习模块。在真实数据集上的大量实验表明，双曲流形是替代欧几里得空间处理跨域推荐任务的有效方案。