Community discovery using nonnegative matrix factorization

Complex networks exist in a wide range of real world systems, such as social networks, technological networks, and biological networks. During the last decades, many researchers have concentrated on exploring some common things contained in those large networks include the small-world property, power-law degree distributions, and network connectivity. In this paper, we will investigate another important issue, community discovery, in network analysis. We choose Nonnegative Matrix Factorization (NMF) as our tool to find the communities because of its powerful interpretability and close relationship between clustering methods. Targeting different types of networks (undirected, directed and compound), we propose three NMF techniques (Symmetric NMF, Asymmetric NMF and Joint NMF). The correctness and convergence properties of those algorithms are also studied. Finally the experiments on real world networks are presented to show the effectiveness of the proposed methods.

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