Communities are often associated with important structural characteristics of a complex network system, therefore detecting communities is considered to be a fundamental problem in network analysis. With the development of data collection technology and platform, more and more sources of network data are acquired, which makes the form of network as well as the related data more complex. To achieve integrative community detection of a multi-layer attributed network that involves multiple network layers together with their attribute data, effectively utilizing the information from the multiple networks and the attributes may greatly enhance the accuracy of community detection. To this end, in this article, we study the integrative community detection problem of a multi-layer attributed network from the perspective of matrix factorization, and propose a penalized alternative factorization (PAF) algorithm to resolve the corresponding optimization problem, followed by the convergence analysis of the PAF algorithm. Results of the numerical study, as well as an empirical analysis, demonstrate the advantages of the PAF algorithm in community discovery accuracy and compatibility with multiple types of network-related data.
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