  Cross-Domain Recommendation (CDR) has been popularly studied to utilize
different domain knowledge to solve the cold-start problem in recommender
systems. Most of the existing CDR models assume that both the source and target
domains share the same overlapped user set for knowledge transfer. However,
only few proportion of users simultaneously activate on both the source and
target domains in practical CDR tasks. In this paper, we focus on the Partially
Overlapped Cross-Domain Recommendation (POCDR) problem, that is, how to
leverage the information of both the overlapped and non-overlapped users to
improve recommendation performance. Existing approaches cannot fully utilize
the useful knowledge behind the non-overlapped users across domains, which
limits the model performance when the majority of users turn out to be
non-overlapped. To address this issue, we propose an end-to-end
dual-autoencoder with Variational Domain-invariant Embedding Alignment (VDEA)
model, a cross-domain recommendation framework for the POCDR problem, which
utilizes dual variational autoencoders with both local and global embedding
alignment for exploiting domain-invariant user embedding. VDEA first adopts
variational inference to capture collaborative user preferences, and then
utilizes Gromov-Wasserstein distribution co-clustering optimal transport to
cluster the users with similar rating interaction behaviors. Our empirical
studies on Douban and Amazon datasets demonstrate that VDEA significantly
outperforms the state-of-the-art models, especially under the POCDR setting.
