Identification of multi-layer networks community by fusing nonnegative matrix factorization and topological structural information

Abstract

The accumulated multi-layer networks in nature and society provide a great opportunity for revealing the mechanisms of the underlying complex systems with multiple types of interactions. Community detection in multi-layer networks aims to extract well-connected groups of vertices for all layers, which shed light into revealing the structure–function relations. The current algorithms either exploit the topological structure of multi-layer networks or explore the latent features of networks, which are criticized due to their low accuracy because they ignore the relation among various layers. To attack these problems, a novel algorithm for Multi-layer community detection by using joint Nonnegative Matrix Factorization (MjNMF) is proposed, which simultaneously considers the topological structure and relations of layers. Specifically, MjNMF extracts features of vertices for each layer by simultaneously factorizing the adjacency matrices of all layers with a common basis matrix, where features of vertices preserve the topological structure of all layers. To obtain community structure, MjNMF decomposes the similarity matrices of vertices for all layers in concern. The smoothness strategy is adopted to connect features of various layers with community structure by learning a project matrix for each layer. Finally, MjNMF integrates feature extraction, community detection, and smoothness by formulating an overall objective function, and derives the optimization rules. The experimental results on ten multi-layer networks demonstrate the proposed algorithm significantly outperforms thirteen state-of-the-art methods in terms of various measurements.