Symmetric Nonnegative Matrix Factorization-Based Community Detection Models and Their Convergence Analysis

Xin Luo, Zhigang Liu, Long Jin, Yue Zhou, Mengchu Zhou

Research output: Contribution to journalArticlepeer-review

92 Scopus citations


Community detection is a popular yet thorny issue in social network analysis. A symmetric and nonnegative matrix factorization (SNMF) model based on a nonnegative multiplicative update (NMU) scheme is frequently adopted to address it. Current research mainly focuses on integrating additional information into it without considering the effects of a learning scheme. This study aims to implement highly accurate community detectors via the connections between an SNMF-based community detector's detection accuracy and an NMU scheme's scaling factor. The main idea is to adjust such scaling factor via a linear or nonlinear strategy, thereby innovatively implementing several scaling-factor-adjusted NMU schemes. They are applied to SNMF and graph-regularized SNMF models to achieve four novel SNMF-based community detectors. Theoretical studies indicate that with the proposed schemes and proper hyperparameter settings, each model can: 1) keep its loss function nonincreasing during its training process and 2) converge to a stationary point. Empirical studies on eight social networks show that they achieve significant accuracy gain in community detection over the state-of-the-art community detectors.

Original languageEnglish (US)
Pages (from-to)1203-1215
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number3
StatePublished - Mar 1 2022

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


  • Community detection
  • convergence analysis
  • graph regularization
  • nonnegative multiplicative update (NMU)
  • social network analysis
  • symmetric and nonnegative matrix factorization (SNMF)


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