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 几何结构保持非负矩阵分解的数据表达方法 Alternative Title A Geometric Structure Preserving Non-negative Matrix Factorization for Data Representation 李冰锋; 唐延东; 韩志 Department 机器人学研究室 Source Publication 信息与控制 ISSN 1002-0411 2017 Volume 46Issue:1Pages:53-59, 64 Indexed By CSCD CSCD ID CSCD:5929439 Contribution Rank 1 Funding Organization 国家自然科学基金资助项目（61303168） Keyword 非负矩阵分解 结构保持 图正则化 补空间 图像聚类 Abstract 作为一种线性降维方法，非负矩阵分解（NMF）算法在多个场合均有应用；但NMF算法只能在欧氏空间上进行语义分解，当输入数据是嵌入在高维空间的低维流形时，NMF会引入较大的分解误差。为解决此问题，本文提出了一种基于几何结构保持的非负矩阵分解算法（SPNMF）。在SPNMF算法中，我们将局部近邻样本点间的相似性关系的保持和远距离非近邻样本点间的互斥性关系的保持引入到NMF框架；并把非负矩阵分解的求解问题转化为数值优化问题，然后用交替优化的方法对SPNMF算法进行了求解。相对于NMF，SPNMF算法拥有更多的数据分布的先验知识，因此SPNMF算法可以获得一种更好低维数据表达方式．在人脸数据库上的试验结果表明，相对于NMF及其它的改进算法，SPNMF算法具有更高的聚类精度。 Other Abstract As a linear dimensionality reduction technique, non-negative matrix factorization (NMF) has been widely used in many fields. However, NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. To address this issue, in this paper, we propose a new non-negative matrix factorization algorithm, known as the structure preserving non-negative matrix factorization (SPNMF). Compared with the existing NMF, our SPNMF method effectively exploits the local affinity structure and distant repulsion structure among data samples. Specifically, we incorporate the local and distant structure preservation terms into the NMF framework and then give an alternative optimization method for SPNMF. Due to prior knowledge from the structure preservation term, SPNMF can learn a good low-dimensional representation. Experimental results on some facial image dataset clustering show the significantly improved performance of SPNMF compared with other state-of-the-art algorithms. Language 中文 Citation statistics Cited Times:1[CSCD]   [CSCD Record] Document Type 期刊论文 Identifier http://ir.sia.cn/handle/173321/20227 Collection 机器人学研究室 Corresponding Author 李冰锋 Affiliation 1.中国科学院沈阳自动化研究所国家重点实验室2.河南理工大学电气工程与自动化学院3.中国科学院大学 Recommended CitationGB/T 7714 李冰锋,唐延东,韩志. 几何结构保持非负矩阵分解的数据表达方法[J]. 信息与控制,2017,46(1):53-59, 64. APA 李冰锋,唐延东,&韩志.(2017).几何结构保持非负矩阵分解的数据表达方法.信息与控制,46(1),53-59, 64. MLA 李冰锋,et al."几何结构保持非负矩阵分解的数据表达方法".信息与控制 46.1(2017):53-59, 64.