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A General Exponential Framework for Dimensionality Reduction
Wang, Su-Jing1,2; Yan, Shuicheng3; Yang, Jian4; Zhou, Chun-Guang2; Fu, Xiaolan1
AbstractAs 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.
KeywordFace recognition manifold learning matrix exponential Laplacian embedding dimensionality reduction
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WOS IDWOS:000329581800034
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Cited Times:40[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.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
First Author Affilication脑与认知科学国家重点实验室
Recommended Citation
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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