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<p>Graph regularized nonnegative matrix factorization(GNMF) was recently established to cope with the extraction of feature representation. Through graph regularization, similar samples remain close in the low-dimensional space, making it suitable for manifold data. However, the existing GNMF methods still have several problems: It is sensitive to data and highly dependent on the quality of data; limited by the linear model, it is unable to directly handle the nonlinear manifold structure; the sparsity property of the solution is neglected in the relevant analysis and modeling process. To address these issues, a novel SemiNMF optimization model, AGNC, is proposed. It utilizes adaptive graph learning to reconstruct the coefficient matrix’s local structure and then applies the N-cut algorithm for clustering. Combining AGNC with SemiNMF, graph regularization, orthogonal subspace, and kernel mapping gives the SemiNMF-KGOSVAGNC framework. This framework adeptly captures the local structural nuances and proficiently addresses the intricacies of semi-nonnegative and nonlinear data. It employs orthogonal subspace constraints with auxiliary variables for sparse, efficient solutions. The iterative update rules are examined, and a convergence proof is provided. Experiments on real-world datasets confirm the algorithm’s excellent clustering ability and superiority over both classical and newly emerged models, advancing image clustering and offering a solution for real-world data challenges.</p>

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A novel optimizing approach for image data clustering based on SemiNMF via adaptive graph and N-cut

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Wen Li,
  • Yasong Chen,
  • Junjian Zhao

摘要

Graph regularized nonnegative matrix factorization(GNMF) was recently established to cope with the extraction of feature representation. Through graph regularization, similar samples remain close in the low-dimensional space, making it suitable for manifold data. However, the existing GNMF methods still have several problems: It is sensitive to data and highly dependent on the quality of data; limited by the linear model, it is unable to directly handle the nonlinear manifold structure; the sparsity property of the solution is neglected in the relevant analysis and modeling process. To address these issues, a novel SemiNMF optimization model, AGNC, is proposed. It utilizes adaptive graph learning to reconstruct the coefficient matrix’s local structure and then applies the N-cut algorithm for clustering. Combining AGNC with SemiNMF, graph regularization, orthogonal subspace, and kernel mapping gives the SemiNMF-KGOSVAGNC framework. This framework adeptly captures the local structural nuances and proficiently addresses the intricacies of semi-nonnegative and nonlinear data. It employs orthogonal subspace constraints with auxiliary variables for sparse, efficient solutions. The iterative update rules are examined, and a convergence proof is provided. Experiments on real-world datasets confirm the algorithm’s excellent clustering ability and superiority over both classical and newly emerged models, advancing image clustering and offering a solution for real-world data challenges.