a new hybrid nmf-based infrastructure for community detection in ‎complex networks

Background and objectives: community detection is a critical problem in ‎investigating complex networks. community detection based on ‎modularity/general modularity density are the popular methods with the ‎advantage of using complex network features and the disadvantage of ‎being np-hard problem for clustering. moreover, non-negative matrix ‎factorization (nmf)-based community detection methods are a family of ‎community detection tools that utilize network topology; but most of ‎them cannot thoroughly exploit network features. in this paper, a hybrid ‎nmf-based community detection infrastructure is developed, including ‎modularity/ general modularity density as more comprehensive indices of ‎networks. the proposed infrastructure enables to solve the challenges of ‎combining the nmf method with modularity/general modularity density ‎criteria and improves the community detection methods for complex ‎networks.‎methods: first, new representations, similar to the model of symmetric ‎nmf, are derived for the model of community detection based on ‎modularity/general modularity density. next, these indices are ‎innovatively augmented to the proposed hybrid nmf-based model as two ‎novel models called ‘general modularity density nmf (gmdnmf) and ‎mixed modularity nmf (mmnmf)’. in order to solve these two np-hard ‎problems, two iterative optimization algorithms are developed.‎results: it is proved that the modularity/general modularity density-‎based community detection can be consistently represented in the form ‎of snmf-based community detection. the performances of the proposed ‎models are verified on various artificial and real-world networks of ‎different sizes. it is shown that mmnmf and gmdnmf models ‎outperform other community detection methods. moreover, the ‎gmdnmf model has better performance with higher computational ‎complexity compared to the mmnmf model.‎conclusion: the results show that the proposed mmnmf model improves ‎the performance of community detection based on nmf by employing ‎the modularity index as a network feature for the nmf model, and the ‎proposed gmdnmf model enhances nmf-based community detection by ‎using the general modularity density index.‎