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几何结构保持非负矩阵分解的数据表达方法
Alternative TitleA 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
ISSN1002-0411
2017
Volume46Issue:1Pages:53-59, 64
Indexed ByCSCD
CSCD IDCSCD:5929439
Contribution Rank1
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 AbstractAs 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
Identifierhttp://ir.sia.cn/handle/173321/20227
Collection机器人学研究室
Corresponding Author李冰锋
Affiliation1.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 Citation
GB/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.
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