hybrid adaptive modularized tri-factor non-negative matrix factorization for community detection in complex networks

Community detection is a significant issue in extracting valuable information and ‎understanding complex network structures. non-negative matrix factorization (nmf) methods ‎are the most remarkable topics in community detection. the modularized tri-factor nmf ‎‎(mtrinmf) method was proposed as a new class of nmf methods that combines the modularized ‎information with tri-factor nmf. it has high computational complexity due to its dependence on ‎the choice of the initial value of the parameter and the number of communities (c). in other ‎words, the mtrinmf method should search among different c candidates to find correct c. in this ‎paper, a novel hybrid adaptive mtrinmf (hamtrinmf) method is proposed to improve the ‎performance of mtrinmf and reduce the computational complexity efficiently. in the proposed ‎method, computational complexity reduction is made by selecting the right c candidates and ‎tuning parameter. for this purpose, a hybrid algorithm including singular value decomposition ‎‎(svd) and relative eigenvalue gap (reg) algorithms is suggested to estimate the set of c ‎candidates. next, the tpmtrinmf model is proposed to improve the performance of community ‎detection via employing a self-tuning β parameter. moreover, experimental results confirm the ‎efficiency of the hamtrinmf method with respect to other reference methods on artificial and ‎real-world networks.‎