Abstract To learn users’ preference, their feedback information is commonly modeled as scalars and integrated into matrix factorization (MF) based algorithms. Based on MF techniques, the preference degree is computed by the product of user and item vectors, which is also represented by scalars. On the contrary, in this paper, we express users’ feedback as constrained vectors, and call the idea constrained preference embedding (CPE); it means that we regard users, items and all users’ behavior as vectors. We find that this viewpoint is more flexible and powerful than traditional MF for item recommendation. For example, by the proposed assumption, users’ heterogeneous actions can be coherently mined because all entities and actions can be transferred to a space of the same dimension. In addition, CPE is able to model the feedback of uncertain preference degree. To test our assumption, we propose two models called CPE-s and CPE-ps based on CPE for item recommendation, and show that the popular pair-wise ranking model BPR-MF can be deduced by some restrictions and variations on CPE-s. In the experiments, we will test CPE and the proposed algorithms, and prove their effectiveness.