Robust Semi-Supervised Community Detection Based on Symmetric Nonnegative Matrix Factorization

Abstract

The symmetric nonnegative matrix factorization (SNMF) model, renowned for its interpretability and efficiency, has been extensively adopted for community detection in the domain of complex networks. However, existing SNMF-based approaches exhibit limitations, particularly in capitalizing on limited supervisory information for enhanced detection performance and in their vulnerability to data distortion due to non-Gaussian noise and outliers. To overcome these limitations, a novel SNMF-based community detection method, namely correntropy-based semi-supervised SNMF (CSSNMF), is proposed in this paper for boosting the performance of SNMF-based methods in community detection tasks. More specifically, CSSNMF is characterized by two principal innovations: 1) adopting the pairwise constraints propagation (PCP) algorithm to fully utilize a small amount of supervisory information for reconstructing a more informative adjacency matrix; 2) using the correntropy instead of the traditional squared Frobenius norm as the similarity measure in SNMF for enhancing the robustness against noise and outliers. Notably, the learned adjacency matrix is not only utilized as the decomposed matrix within the SNMF model, but also integrated into the graph regularization for deriving a discriminative community indicator matrix.Moreover, the proposed method is delved into a thorough analysis, considering aspects of convergence, the influence of supervisory information, and computational complexity. Through extensive experimental evaluations, the superiority of CSSNMF in terms of effectiveness and robustness has been demonstrated in community detection applications, particularly when benchmarked against several leading SNMF-based methods on real-world networks with and without significant noise interference.

Keywords: Symmetric nonnegative matrix factorization, semi-supervised learning, robustness, community detection.