Abstract
Knowing the number of communities in the complex networks can have a great impact on the community detection process and can be considered a critical parameter for most community detection algorithms. Nonnegative matrix tri-factorization (NMTF) is another type of nonnegative matrix factorization (NMF) method that considers the interactions among communities and has high interpretability and accuracy in community detection. Whereas community detection is an NP-hard problem, applying evolutionary algorithms is favored rather than classical methods. In the proposed approach, the number of communities in a network is heuristically examined based on the network topology structure. The genetic algorithm (GA) is one of the most widely accepted optimizing techniques and the oldest evolutionary algorithm which optimizes various issues. In this paper, first, a symmetric nonnegative matrix tri-factorization (SNMTF) is presented to detect communities as an optimization problem in complex networks, because most complex networks are symmetric. The projected gradient descent method is applied to the SNMTF algorithm (PGD-SNMTF) to improve efficiency. Then the GA is used for optimizing the factorization process and estimating the number of communities in the complex networks. Finally, the accuracy of the proposed method is evaluated based on the results obtained and the expected number of communities in the networks. In addition, the proposed approach is compared to other common methods such as elbow, silhouette, rule of thumb, and eigen-gap methods for estimating the number of communities in complex networks. The results of the proposed method indicate high efficiency and accuracy in estimating the number of communities in the investigated networks.
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Jouyban, M., Hosseini, S. A new approach for estimating the number of communities in complex networks using PGD-SNMTF and GA. Evolving Systems 15, 591–609 (2024). https://doi.org/10.1007/s12530-023-09530-z
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DOI: https://doi.org/10.1007/s12530-023-09530-z