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.‎