Abstract Community detection is of crucial importance in understanding structures of complex networks. In many real-world networks, communities naturally overlap since a node usually has multiple community memberships. One popular technique to cope with overlapping community detection is Matrix Factorization (MF). However, existing MFbased models have ignored the fact that besides neighbors, “local non-neighbors” (e.g., my friend’s friend but not my direct friend) are helpful when discovering communities. In this paper, we propose a Locality-based Non-negative Matrix Factorization (LNMF) model to refine a preference-based model by incorporating locality into learning objective. We define a subgraph called “k-degree local network” to set a boundary between local nonneighbors and other non-neighbors. By discriminately treating these two class of non-neighbors, our model is able to capture the process of community formation. We propose a fast sampling strategy within the stochastic gradient descent based learning algorithm. We compare our LNMF model with several baseline methods on various real-world networks, including large ones with ground-truth communities. Results show that our model outperforms state-of-the-art approaches.