Non-negative matrix factorization for overlapping community detection in directed weighted networks with sparse constraints

Detecting overlapping communities is essential for analyzing the structure and function of complex networks. However, most existing approaches only consider network topology and overlook the benefits of attribute information. In this paper, we propose a novel attribute-information non-negative matrix factorization approach that integrates sparse constraints and optimizes an objective function for detecting communities in directed weighted networks. Our algorithm updates the basic non-negative matrix adaptively, incorporating both network topology and attribute information. We also add a sparsity constraint term of graph regularization to maintain the intrinsic geometric structure between nodes. Importantly, we provide strict proof of convergence for the multiplication update rule used in our algorithm. We apply our proposed algorithm to various artificial and real-world networks and show that it is more effective for detecting overlapping communities. Furthermore, our study uncovers the intricate iterative process of system evolution toward convergence and investigates the impact of various variables on network detection. These findings provide insights into building more robust and operable complex systems.