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چکیده
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analysis, bioinformatics, and image recognition. Symmetric Nonnegative Matrix Factorization (SNMF) has emerged as a powerful tool for community detection by decomposing similarity matrices. However, traditional SNMF methods often struggle with real-world data due to their sensitivity to noise, outliers, and imperfect similarity measures, which can compromise clustering accuracy. To address these challenges, we propose Graph-Regularized Weighted SNMF (GWSNMF), a novel framework that introduces three key innovations: (1) a graph-regularized symmetric factorization that preserves both global and local structural relationships; (2) an optimizable weighted norm that automatically reduces the influence of outliers; and (3) an entropy-regularized weighting scheme that enhances the model’s ability to capture meaningful patterns in noisy data. Unlike traditional SNMF, GWSNMF integrates an optimized adjacency graph construction and a weighted Frobenius norm to improve robustness and accuracy. The proposed framework generalizes existing techniques, including NMF, spectral clustering, and their variants, while offering superior performance in noisy or high-dimensional settings. Extensive experiments on six benchmark datasets demonstrate that GWSNMF consistently outperforms state-of-the-art clustering methods in terms of accuracy and normalized mutual information. Theoretical analysis guarantees convergence, and practical results validate the model’s efficiency and scalability.
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