稀疏诱导流形正则化凸非负矩阵分解算法

邱飞岳; 陈博文; 陈铁明; 章国道

doi:10.11959/j.issn.1000-436x.2020064

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稀疏诱导流形正则化凸非负矩阵分解算法

学术论文 | 更新时间：2024-06-05

- 稀疏诱导流形正则化凸非负矩阵分解算法
- Sparsity induced convex nonnegative matrix factorization algorithm with manifold regularization
- 通信学报 2020年41卷第5期页码：84-95
- 作者机构：
  
  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
- 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" ]
- 基金信息：
  
  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)
- DOI：10.11959/j.issn.1000-436x.2020064
  中图分类号： TP181
- 网络出版日期：2020-05，
  
  纸质出版日期：2020-05-25
- 稿件说明：
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邱飞岳, 陈博文, 陈铁明, 等. 稀疏诱导流形正则化凸非负矩阵分解算法[J]. 通信学报, 2020,41(5):84-95.

Feiyue QIU, Bowen CHEN, Tieming CHEN, et al. Sparsity induced convex nonnegative matrix factorization algorithm with manifold regularization[J]. Journal on communications, 2020, 41(5): 84-95.
邱飞岳, 陈博文, 陈铁明, 等. 稀疏诱导流形正则化凸非负矩阵分解算法[J]. 通信学报, 2020,41(5):84-95. DOI： 10.11959/j.issn.1000-436x.2020064.

Feiyue QIU, Bowen CHEN, Tieming CHEN, et al. Sparsity induced convex nonnegative matrix factorization algorithm with manifold regularization[J]. Journal on communications, 2020, 41(5): 84-95. DOI： 10.11959/j.issn.1000-436x.2020064.

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。

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.

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