计算机科学与探索2026，Vol.20Issue(4)：1061-1078,18.DOI:10.3778/j.issn.1673-9418.2505045
基于双图正则化的鲁棒非负矩阵分解聚类算法
Robust Non-negative Matrix Factorization Clustering Algorithm with Dual-Graph Regularization
摘要
Abstract
Non-negative matrix factorization(NMF),as an effective approach for data representation and dimensionality reduction,has been extensively utilized in domains such as image processing and text clustering.Nevertheless,the standard NMF,which is only capable of handling non-negative data,is sensitive to outliers and noise,and fails to fully capture the manifold information concealed in the sample space and feature space.To obtain superior clustering performance based on Semi-NMF,feature manifold,sample manifold,and robustness,this paper proposes a robust non-negative matrix factorization clustering algorithm based on dual-graph regularization(DGRNMF).By using the L2,1 norm to enhance the robustness of NMF against outliers or noise,and introducing sample graphs and feature graphs for regularization to preserve the local geometric structure of the data space,the dimensionally-reduced representation not only maintains the local neighbor relationships between samples but also retains the intrinsic correlations between features.It also imposes sparse constraints on the decomposition error to reduce the influence of outliers and noise on the global optimization objective.Meanwhile,semi-nonnegative matrix factorization is adopted to handle mixed data,thereby expanding the applicability of the algorithm to mixed symbolic data in the real world.The convergence of the proposed algorithm has been verified through theoretical and empirical analysis.This paper conducts clustering experiments on 12 public datasets,covering various data types such as face images and text.The experimental results show that the DGRNMF algorithm out-performs other classic clustering algorithms,demonstrating significant advantages in clustering accuracy and robustness,providing new ideas for expanding the application of NMF in complex real-world scenarios.关键词
半非负矩阵/鲁棒性/双图正则化/稀疏约束/聚类Key words
semi-nonnegative matrix/robustness/dual-graph regularization/sparsity constraint/clustering分类
信息技术与安全科学引用本文复制引用
高海燕,刘孟淑,周改改,钟灵..基于双图正则化的鲁棒非负矩阵分解聚类算法[J].计算机科学与探索,2026,20(4):1061-1078,18.基金项目
国家社会科学基金(19XTJ002) （19XTJ002）
甘肃省自然科学基金(23JRRA1186) （23JRRA1186）
全国统计科学研究重点项目(2025LZ007) （2025LZ007）
甘肃省高校青年博士支持项目(2025QB-058) （2025QB-058）
甘肃省高校研究生"创新之星"项目(2025CXZX-897).This work was supported by the National Social Science Foundation of China(19XTJ002),the Natural Science Foundation of Gansu Province(23JRRA1186),the National Key Statistical Science Research Project(2025LZ007),the Young Doctor Support Program of Gansu Provincial Universities(2025QB-058),and the Gansu Provincial Graduate Student"Innovation Star"Program(2025CXZX-897). （2025CXZX-897）
