Identification of key nodes in complex networks by using a joint technique of nonnegative matrix factorization and regularization

Identifying key nodes in complex networks is essential to deeply understand and fully utilize the properties and functions of complex systems. Currently, existing traditional methods perform critical nodes identification by manually selecting important attribute features of nodes, but there are limitations in this approach. Manual selection of attribute features may overlook non -obvious features related to nodes criticality and correlations between attribute features. To compensate for the shortcomings of traditional methods, a Joint Technique for identifying critical nodes, called JTNMFR, is presented based on Nonnegative Matrix Factorization and Regularization. Factorization of weighted adjacency matrix is performed to obtain potential attribute features of nodes, and communicability network matrix and similarity matrix are introduced as regularization terms to control sparsity of the decomposition results. Ultimately, the importance of nodes is assessed by constructing an objective function that integrates these two aspects and utilizing alternative iteration to obtain the attribute matrix. To validate the accuracy and reliability of JTNMFR, we compare it with nine other identification approaches on eight real networks. Experimental results show that JTNMFR not only significantly outperforms the other algorithms in terms of accuracy of node importance, monotonicity, and node spreading ability but also provides a more accurate means of assessing node importance.