A Symmetry and Graph Regularized Nonnegative Matrix Factorization Model for Community Detection

TL;DR

This paper introduces SGNMF, a novel community detection model for large-scale undirected networks that enhances representation learning by using multiple latent matrices, enforces symmetry, and incorporates graph regularization.

Contribution

It proposes a new SGNMF model that improves community detection by leveraging multiple latent matrices, symmetry regularization, and graph regularization, with proven convergence and superior experimental results.

Findings

SGNMF outperforms baseline models in community detection accuracy.

The model effectively captures network symmetry and intrinsic geometry.

Theoretical convergence of SGNMF is established.

Abstract

Community is a fundamental and critical characteristic of a Large-scale Undirected Network (LUN) like a social network, making community detection a vital yet thorny issue in LUN representation learning. Owing to its good scalability and interpretability, a Symmetric and Nonnegative Matrix Factorization (SNMF) model is commonly used to tackle this issue. However, it adopts a unique Latent Factor (LF) matrix for precisely representing an LUN's symmetry, which leads to a reduced LF space that impairs its representational learning ability. Motivated by this discovery, this study proposes a Symmetry and Graph-regularized Nonnegative Matrix Factorization (SGNMF) method that adopts three-fold ideas: a) leveraging multiple LF matrices to represent an LUN, thereby enhancing its representation learning ability; b) introducing a symmetry regularization term that implies the equality constraint between its multiple LF matrices, thereby illustrating an LUN's symmetry; and c) incorporating graph regularization into its learning objective, thereby illustrating an LUN's intrinsic geometry. A theoretical proof is provided to ensure SGNMF's convergence on an LUN. Extensive experiment results on ten LUNs from real applications demonstrate that our proposed SGNMF-based community detector significantly outperforms several baseline and state-of-the-art models in achieving highly-accurate results for community detection.