Modularized convex nonnegative matrix factorization for community detection in signed and unsigned networks

NMF-based models in unsigned networks, the links of which are positive links only, have been applied in many aspects, such as community detection, link prediction, etc. However, NMF has been under-explored for community discovery in signed networks due to its constraint of non-negativity. Also, there are few related studies which could find out accurate partitions on both signed and unsigned networks due to their difference of community structure. In this paper, we propose a novel modularized convex nonnegative matrix factorization model which combines signed modularized information with convex NMF model, improving the accuracy of community detection in signed and unsigned networks. As for model selection, we extend the modularity density to signed networks and employ the signed modularity density to determine the number of communities automatically. Finally, the effectiveness of our model is verified on both synthetic and real-world networks. •A modularized convex nonnegative matrix factorization model (MCNMF) is proposed.•Signed modularity density (SMD) is proposed to infer the number of communities on both signed and unsigned networks.•The effectiveness and the superiority of MCNMF and SMD are verified on synthetic and real signed and unsigned networks.