Abstract: To address the limitations of existing non-negative matrix factorization(NMF)-based community detection methods,such as the requirement for preset the number of communities,susceptibility to local optima,and limited model generalization,this paper proposes Adp-NMTF,an adaptive community detection algorithm based on non-negative matrix tri-factorization(NMTF).The algorithm incorporates a dynamic evaluation and feedback mechanism to automatically search and determine the optimal number of communities without manual intervention.It introduces graph regularization,sparsity constraints,and inter-community independence constraints to balance generalization capability and interpretability.Additionally,semi-supervised initialization and warm-start strategies are employed to accelerate NMTF convergence and improve computational efficiency.Experimental results demonstrate that Adp-NMTF can autonomously determine a reasonable number of communities and outperforms mainstream baseline methods in both synthetic and real-world networks across evaluation metrics including modularity(Q),normalized mutual information(NMI),and adjusted Rand index(ARI).Furthermore,the convergence rate of matrix factorization is significantly improved.

Key words: Complex networks, Community detection, Non-negative matrix factorization, Non-negative matrix tri-factorization, Regularization constraints