Quantum mechanics

Detector

Algorithm

Stationary point

Convergence (economics)

Eigenvalues and eigenvectors

Telecommunications

Economics

Computer science

Mathematical optimization

Scaling

Non-negative matrix factorization

Physics

Nonlinear system

Mathematics

Hyperparameter

Mathematical analysis

Artificial intelligence

Geometry

Multiplicative function

Economic growth

Matrix decomposition

Machine learning

IEEE Transactions on Neural Networks and Learning Systems

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.

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