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<p>Graph clustering is a crucial technique in network analysis for discovering latent group structures within complex graphs. However, traditional clustering approaches based on Nonnegative Matrix Factorization (NMF) often suffer from sensitivity to noise, outliers, and the inability to capture nonlinear structural patterns. To overcome these challenges, we propose a Robust Matrix Factorization framework based on Singular Value Decomposition (RMFSVD) for accurate and noise-resilient graph clustering. RMFSVD leverages a low-rank approximation scheme with robust singular value decomposition techniques to effectively extract meaningful latent features while enhancing resilience to noisy and incomplete data. Specifically, RMFSVD decomposes the input similarity matrix into a clean low-rank component and a sparse noise matrix, enabling effective separation of structural information from noise. In addition, RMFSVD employs a graph-boosting strategy to reinforce and improve the modeling of inter-node relationships across the network. Extensive experiments on multiple benchmark graph datasets demonstrate that RMFSVD outperforms existing state-of-the-art clustering methods in terms of robustness, scalability, and clustering performance.</p>

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RMFSVD: robust graph clustering based on matrix factorization and singular value decomposition

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Yingchao Zhen,
  • Jiamao Han,
  • Yaxing Wei,
  • Qi Guo,
  • Amin Rezaei

摘要

Graph clustering is a crucial technique in network analysis for discovering latent group structures within complex graphs. However, traditional clustering approaches based on Nonnegative Matrix Factorization (NMF) often suffer from sensitivity to noise, outliers, and the inability to capture nonlinear structural patterns. To overcome these challenges, we propose a Robust Matrix Factorization framework based on Singular Value Decomposition (RMFSVD) for accurate and noise-resilient graph clustering. RMFSVD leverages a low-rank approximation scheme with robust singular value decomposition techniques to effectively extract meaningful latent features while enhancing resilience to noisy and incomplete data. Specifically, RMFSVD decomposes the input similarity matrix into a clean low-rank component and a sparse noise matrix, enabling effective separation of structural information from noise. In addition, RMFSVD employs a graph-boosting strategy to reinforce and improve the modeling of inter-node relationships across the network. Extensive experiments on multiple benchmark graph datasets demonstrate that RMFSVD outperforms existing state-of-the-art clustering methods in terms of robustness, scalability, and clustering performance.