Community Detection in Multi-Layer Networks Using Joint Nonnegative Matrix Factorization

Abstract

Listen

Translate article

Many complex systems are composed of coupled networks through different layers, where each layer represents one of many possible types of interactions. A fundamental question is how to extract communities in multi-layer networks. The current algorithms either collapses multi-layer networks into a single-layer network or extends the algorithms for single-layer networks by using consensus clustering. However, these approaches have been criticized for ignoring the connection among various layers, thereby resulting in low accuracy. To attack this problem, a quantitative function (multi-layer modularity density) is proposed for community detection in multi-layer networks. Afterward, we prove that the trace optimization of multi-layer modularity density is equivalent to the objective functions of algorithms, such as kernel $K$ -means, nonnegative matrix factorization (NMF), spectral clustering and multi-view clustering, for multi-layer networks, which serves as the theoretical foundation for designing algorithms for community detection. Furthermore, a S emi- S upervised j oint N onnegative M atrix F actorization algorithm ( S2-jNMF ) is developed by simultaneously factorizing matrices that are associated with multi-layer networks. Unlike the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the S2-jNMF algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method outperforms the state-of-the-art approaches for community detection in multi-layer networks.