Abstract Real-world data are seldom unstructured, yet traditional Matrix Factorization (MF) models, as one of the most powerful collaborative filtering approaches, generally rely on this assumption to recover the low-rank structures for recommendation. However, few of them are able to explicitly consider structured constraint with the underlying low-rank assumption to model complex user interests. To solve this problem, we propose a unified MF framework with generalized Laplacian constraint for collaborative filtering. We investigate the connection between the recently proposed Laplacian constraint and the classical normalized cut problem, and make it possible to extend the original non-overlapping prior, to capture the overlapping case via learning the decomposed multi-facet graphs. Experiments on realworld datasets demonstrate the effectiveness of the proposed method.