  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.
