Community detection in social network with pairwisely constrained symmetric non-negative matrix factorization

Non-negative Matrix Factorization (NMF) aims to find two non-negative matrices whose product approximates the original matrix well, and is widely used in clustering condition with good physical interpretability and universal applicability. Detecting communities with NMF can keep non-negative network physical definition and effectively capture communities-based structure in the low dimensional data space. However some NMF methods in community detection did not concern with more network inner structures or existing ground-truth community information. In this paper, we propose a novel pairwisely constrained non-negative symmetric matrix factorization (PCSNMF) method, which not only consider symmetric community structures of undirected network, but also takes into consideration the pairwise constraints generated from some ground-truth group information to enhance the community detection. We compare our approaches with other NMF-based methods in three social networks, and experimental results for community detection show that our approaches are all feasible and achieve better community detection results.