A novel semi-supervised clustering method for complex network based ‎on modularity

Clustering or community detection is a powerfrul tool for ‎analayzing complex networks which is widely used for ‎modeling complex systems. Modularity is a ‎comprehensive criterion for evaluating the quality of ‎clusters (or communities). However, it has some ‎limitations and challenges such as being a NP-hard ‎problem and not using prior information. So, Modularity-‎based community detection cannot be extended as a ‎semi-supervised community detection method. On the ‎other hand, one of the most common semi-supervised ‎methods which can use prior knowledge for clustering is ‎community detection based on non negative matrix ‎factorization (NMF). But, this method is not able to ‎consider the features of the networks. Therefore, in this ‎paper to overcome the mentioned limitations and ‎challenges and by presenting a new proof, a structure ‎similar to community detection based on NMF is ‎presented for modularity-based community detection ‎which can employ prior knowledge and iterative ‎solution. Therefore, a novel semi-supervised community ‎detection based on modularity (SSNMF-Q) criteria is ‎developed by utilizing prior information and iterative ‎solution instead of solving a NP-hard problem. To ‎evaluate SSNMF-Q, five real world networks are used ‎and it is shown that the SSNMF-Q had better ‎performance compared to other semi-supervised ‎community detection methods based on NMF.‎