Combinatorics

Physics

Factorization

Matrix algebra

Mathematics

Symmetric matrix

Algorithm

Matrix (chemical analysis)

Nonnegative matrix

Non-negative matrix factorization

Eigenvalues and eigenvectors

Composite material

Materials science

Computer science

Quantum mechanics

Complex network

Matrix decomposition

IEEE Transactions on Computational Social Systems

Community detection is one of the popular research topics in the field of complex networks analysis. It aims to identify communities, represented as cohesive subgroups or clusters, where nodes in the same community link to each other more densely than others outside. Due to the interpretability, simplicity, flexibility, and generality, nonnegative matrix factorization (NMF) has become a very ideal model for community detection and lots of related methods have been presented. To facilitate research on NMF-based community detection, in this article, we make a comprehensive review on NMF-based methods for community detection, especially the state-of-the-art methods presented in high prestige journals or conferences. First, we introduce the basic principles of NMF and explain why NMF can detect communities and design a general framework of NMF-based community detection. Second, according to the applicable network types, we propose a taxonomy to divide the existing NMF-based methods for community detection into six categories, namely, topology networks, signed networks, attributed networks, multilayer networks, dynamic networks, and large-scale networks. We deeply analyze representative methods in every category. Finally, we summarize the common problems faced by all methods and potential solutions and propose four promising research directions. We believe that this survey can fully demonstrate the versatility of NMF-based community detection and serve as a useful guideline for researchers in related fields.

A Survey of Community Detection in Complex Networks Using Nonnegative Matrix Factorization