Recommender systems research has experienced different stages such as from user preference understanding to content analysis. Typical recommendation algorithms were built on the following bases: (1) assuming users and items are IID, namely independent and identically distributed, and (2) focusing on specific aspects such as user preferences or contents. In reality, complex recommendation tasks involve and request (1) personalized outcomes to tailor heterogeneous subjective preferences; and (2) explicit and implicit objective coupling relationships between users, items, and ratings to be considered as intrinsic forces driving preferences. This inevitably involves the non-IID complexity and the need of combining subjective preference with objective couplings hidden in recommendation applications. In this paper, we propose a novel generic coupled matrix factorization (CMF) model by incorporating non-IID coupling relations between users and items. Such couplings integrate the intra-coupled interactions within an attribute and inter-coupled interactions among different attributes. Experimental results on two open data sets demonstrate that the user/item couplings can be effectively applied in RS and CMF outperforms the benchmark methods.