A General Exponential Framework for Dimensionality Reduction

doi:10.1109/TIP.2013.2297020

	A General Exponential Framework for Dimensionality Reduction
	Wang,Su-Jing 1,2; Yan,Shuicheng 3; Yang,Jian 4; Zhou,Chun-Guang 2; Fu,Xiaolan1
第一作者	Wang, Su-Jing
通讯作者邮箱	wangsujing@psych.ac.cn ; eleyans@nus.edu.sg ; csjyang@mail.njust.edu.cn ; cgzhou@jlu.edu.cn ; fuxl@psych.ac.cn
心理所单位排序	1
摘要	As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e. g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.
关键词	Face recognition manifold learning matrix exponential Laplacian embedding dimensionality reduction
学科领域	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
	2014-02-01
语种	英语
DOI	10.1109/TIP.2013.2297020
发表期刊	IEEE TRANSACTIONS ON IMAGE PROCESSING
ISSN	1057-7149
卷号	23 期号:2 页码:920-930
期刊论文类型	Article
URL	查看原文
收录类别	SCI
WOS关键词	LINEAR DISCRIMINANT-ANALYSIS ; PRESERVING PROJECTIONS ; FACE ; MATRIX ; EIGENFACES ; ALGORITHM ; COMPUTE
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS记录号	WOS:000329581800034
WOS分区	Q1
引用统计	被引频次：59[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.psych.ac.cn/handle/311026/14174
专题	脑与认知科学国家重点实验室
作者单位	1.Chinese Acad Sci, Inst Psychol, State Key Lab Brain & Cognit Sci, Beijing 100101, Peoples R China; 2.Jilin Univ, Coll Comp Sci & Technol, Changchun 130012, Peoples R China; 3.Natl Univ Singapore, Dept Elect & Comp Engn, Singapore 119077, Singapore; 4.Nanjing Univ Sci & Technol, Sch Comp Sci & Technol, Nanjing 210094, Jiangsu, Peoples R China
第一作者单位	脑与认知科学国家重点实验室
推荐引用方式 GB/T 7714	Wang,Su-Jing,Yan,Shuicheng,Yang,Jian,et al. A General Exponential Framework for Dimensionality Reduction[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING,2014,23(2):920-930.
APA	Wang,Su-Jing,Yan,Shuicheng,Yang,Jian,Zhou,Chun-Guang,&Fu,Xiaolan.(2014).A General Exponential Framework for Dimensionality Reduction.IEEE TRANSACTIONS ON IMAGE PROCESSING,23(2),920-930.
MLA	Wang,Su-Jing,et al."A General Exponential Framework for Dimensionality Reduction".IEEE TRANSACTIONS ON IMAGE PROCESSING 23.2(2014):920-930.

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