Clustering of multi-layer networks with structural relations and conservation of features

Abstract

Multi-layer networks are omnipresent in nature and society, as complex systems often involve multiple types of relationships among entities. Compared with single-layer graphs, community detection is a challenging task that requires simultaneous characterization of the structure and relations across various layers. Current algorithms have been criticized for their suboptimal performance in describing and quantifying the structure of communities in multi-layer networks. A novel algorithm, called McNMF, is proposed to detect the conserved communities in multi-layer networks, where the shared and layer-specific features of vertices are learned simultaneously by utilizing joint nonnegative matrix factorization. Specifically, McNMF joins the feature learning, feature decomposition, and relation of the shared and layer-specific features into an overall objective function, thereby enhancing the quality of features. To learn the features of vertices, McNMF jointly factorizes matrices associated with multi-layer networks by projecting the topology into different basis spaces. It then decomposes the learned features into shared and layer-specific parts, enabling quantification of multi-layer network specificity at the feature level. Moreover, the relation between the shared and layer-specific features of vertices is measured using trace optimization, providing a comprehensive strategy to characterize the structure of conserved communities in multi-layer networks. Extensive experiments on artificial and real-world multi-layer networks demonstrate that the proposed algorithm significantly outperforms state-of-the-art methods in terms of accuracy.