Balanced symmetric non-negative matrix factorization

Symmetric non-negative matrix factorization (SNMF) as a classical graph clustering method has demonstrated powerful clustering capabilities in an increasing number of studies. However, improper initialization may cause the algorithm to get stuck in a local optimum, resulting in a highly uneven distribution of samples across clusters. To address the problem, we propose a Balanced Symmetric Non-negative Matrix Factorization (BSNMF) model that introduces a novel balance-regularization term to actively equalize cluster sizes and boost clustering performance. The proposed BSNMF incorporates a newly designed balance-regularization term that encourages more balanced cluster distributions to enhance clustering performance. Projection Gradient Descent (PGD) is employed to solve this optimization problem. Experiments conducted on eight benchmark datasets demonstrate the effectiveness of our algorithm.