User Distribution Mapping Modelling with Collaborative Filtering for Cross Domain Recommendation

User cold-start recommendation aims to provide accurate items for the newly joint users and is a hot and challenging problem. Nowadays as people participant in different domains, how to recommend items in the new domain for users in an old domain has become more urgent. In this paper, we focus on the Dual Cold-Start Cross Domain Recommendation (Dual-CSCDR) problem. That is, providing the most relevant items for new users on the source and target domains. The prime task in Dual-CSCDR is to properly model user-item rating interactions and map user expressive embeddings across domains. However, previous approaches cannot solve Dual-CSCDR well, since they separate the collaborative filtering and distribution mapping process, leading to the error superimposition issue. Moreover, most of these methods fail to fully exploit the cross-domain relationship among large number of non-overlapped users, which strongly limits their performance. To fill this gap, we propose User Distribution Mapping model with Collaborative Filtering (UDMCF), a novel end-to-end cold-start cross-domain recommendation framework for the Dual-CSCDR problem. UDMCF includes two main modules, i.e., rating prediction module and distribution alignment module. The former module adopts one-hot ID vectors and multi-hot historical ratings for collaborative filtering via a contrastive loss. The latter module contains overlapped user embedding alignment and general user subgroup distribution alignment. Specifically, we innovatively propose unbalance distribution optimal transport with typical subgroup discovering algorithm to map the whole user distributions. Our empirical study on several datasets demonstrates that UDMCF significantly outperforms the state-of-the-art models under the Dual-CSCDR setting.