Overlapping community detection via bounded nonnegative matrix tri-factorization

Complex networks are ubiquitous in our daily life, with the World Wide Web, social networks, and academic citation networks being some of the common examples. It is well understood that modeling and understanding the network structure is of crucial importance to revealing the network functions. One important problem, known as community detection, is to detect and extract the community structure of networks. More recently, the focus in this research topic has been switched to the detection of overlapping communities. In this paper, based on the matrix factorization approach, we propose a method called bounded nonnegative matrix tri-factorization (BNMTF). Using three factors in the factorization, we can explicitly model and learn the community membership of each node as well as the interaction among communities. Based on a unified formulation for both directed and undirected networks, the optimization problem underlying BNMTF can use either the squared loss or the generalized KL-divergence as its loss function. In addition, to address the sparsity problem as a result of missing edges, we also propose another setting in which the loss function is defined only on the observed edges. We report some experiments on real-world datasets to demonstrate the superiority of BNMTF over other related matrix factorization methods.