通信学报 ›› 2020, Vol. 41 ›› Issue (5): 84-95.doi: 10.11959/j.issn.1000-436x.2020064

• 学术论文 • 上一篇    下一篇

稀疏诱导流形正则化凸非负矩阵分解算法

邱飞岳1,2,陈博文2,陈铁明2,章国道2   

  1. 1 浙江工业大学教育科学与技术学院,浙江 杭州 310023
    2 浙江工业大学计算机科学与技术学院,浙江 杭州 310023
  • 修回日期:2020-03-04 出版日期:2020-05-25 发布日期:2020-05-30
  • 作者简介:邱飞岳(1965- ),男,浙江诸暨人,博士,浙江工业大学教授、博士生导师,主要研究方向为智能计算、机器学习、虚拟现实等|陈博文(1996- ),男,安徽合肥人,浙江工业大学硕士生,主要研究方向为机器学习与虚拟现实等|陈铁明(1978- ),男,浙江诸暨人,博士,浙江工业大学教授、博士生导师,主要研究方向为网络空间安全与大数据智能分析等|章国道(1988- ),男,浙江衢州人,浙江工业大学博士生,主要研究方向为数据挖掘
  • 基金资助:
    浙江省自然科学基金资助项目(LQ20F020014);浙江省重点研发计划基金资助项目(2018C01080);国家自然科学基金资助项目(61472366);国家自然科学基金资助项目(61379077)

Sparsity induced convex nonnegative matrix factorization algorithm with manifold regularization

Feiyue QIU1,2,Bowen CHEN2,Tieming CHEN2,Guodao ZHANG2   

  1. 1 College of Education Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China
    2 College of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China
  • Revised:2020-03-04 Online:2020-05-25 Published:2020-05-30
  • Supported by:
    The Natural Science Foundation of Zhejiang Province(LQ20F020014);The Key Technologies Research and Development Program of Zhejiang Province(2018C01080);The National Natural Science Foundation of China(61472366);The National Natural Science Foundation of China(61379077)

摘要:

针对非负矩阵分解方法在有噪声的真实数据中获得特征的有效性问题,提出了一种稀疏诱导的流形正则化凸非负矩阵分解算法。所提算法在流形正则化的基础上,向低维子空间的基矩阵添加基于L<sub>2,1</sub>范数的稀疏约束,构建了乘法更新规则,分析在该规则下算法的收敛性,并设计了在低维子空间上不同噪声环境下的聚类实验。K均值聚类实验结果表明,稀疏约束降低了噪声特征在学习中的表达能力,所提算法在不同程度上优于同类8种算法,对噪声有更强的稳健性。

关键词: 非负矩阵分解, 流形正则化, 稀疏约束, K均值聚类

Abstract:

To address problems that the effectiveness of feature learned from real noisy data by classical nonnegative matrix factorization method,a novel sparsity induced manifold regularized convex nonnegative matrix factorization algorithm (SGCNMF) was proposed.Based on manifold regularization,the L<sub>2,1</sub>norm was introduced to the basis matrix of low dimensional subspace as sparse constraint.The multiplicative update rules were given and the convergence of the algorithm was analyzed.Clustering experiment was designed to verify the effectiveness of learned features within various of noisy environments.The empirical study based on K-means clustering shows that the sparse constraint reduces the representation of noisy features and the new method is better than the 8 similar algorithms with stronger robustness to a variable extent.

Key words: nonnegative matrix factorization, manifold regularization, sparse constraint, K-means clustering

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