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几何结构保持非负矩阵分解的数据表达方法
A Geometric Structure Preserving Non-negative Matrix Factorization for Data Representation

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文摘 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.
其他语种文摘 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 nonnegative 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.
来源 信息与控制 ,2017,46(1):53-59,64 【核心库】
DOI 10.13976/j.cnki.xk.2017.0053
关键词 非负矩阵分解 ; 结构保持 ; 图正则化 ; 补空间 ; 图像聚类
地址

中国科学院沈阳自动化研究所国家重点实验室, 辽宁, 沈阳, 110016

语种 中文
文献类型 研究性论文
ISSN 1002-0411
学科 自动化技术、计算机技术
基金 国家自然科学基金资助项目
文献收藏号 CSCD:5929439

参考文献 共 21 共2页

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引证文献 1 篇

1 熊鹤 基于投影梯度方法的鲁棒流形非负矩阵分解算法 信息与控制,2018,47(2):166-175
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