Overlapping community detection with preference and locality information: a non-negative matrix factorization approach

Community detection plays an important role in understanding structures and patterns in complex networks. In real-world networks, a node in most cases belongs to multiple communities, which makes communities overlap with each other. One popular technique to cope with overlapping community detection is matrix factorization (MF). However, existing MF approaches only make use of the existence of a link, but ignore the implicit preference information inside it. In this paper, we first propose a Preference-based Non-negative Matrix Factorization (PNMF) model to take link preference information into consideration. Distinguished from traditional value approximation-based matrix factorization approaches, our model maximizes the likelihood of the preference order for each node so that it overcomes the indiscriminate penalty problem in which non-linked pairs inside one community are equally penalized in objective functions as those across two communities. Moreover, we propose a Locality-based Non-negative Matrix Factorization (LNMF) model to further incorporate the concept of locality and generalize the preference system of PNMF. Particularly, we define a subgraph called “K-degree local network” to set a boundary between local non-neighbors and other non-neighbors, and explicitly treat these two classes of non-neighbors in objective function. Through experiments on various benchmark networks, we show that our PNMF model outperforms state-of-the-art baselines, and the generalized LNMF model further performs better than the PNMF model on datasets with high locality.