Many real-life datasets exhibit structure in the form of physically meaningful clusters - e.g., news documents can be categorized as sports, politics, entertainment, and so on. Taking these clusters into account together with low-rank structure may yield parsimonious matrix and tensor factorization models and more powerful data analytics. Prior works made use of data-domain similarity to improve nonnegative matrix factorization. Here we are instead interested in joint low-rank factorization and latent-domain clustering; that is, in clustering the latent reduced-dimension representations of the observed entities. A unified algorithmic framework that can deal with both matrix and tensor factorization and latent clustering is proposed. Numerical results obtained from synthetic and real document data show that the proposed approach can significantly improve factor analysis and clustering accuracy.