An Explicit Nonlinear Mapping for Manifold Learning

CASIA OpenIR > 多模态人工智能系统全国重点实验室 > 机器人理论与应用

	An Explicit Nonlinear Mapping for Manifold Learning
	Qiao, Hong1 ; Zhang, Peng 2; Wang, Di 3,4; Zhang, Bo 4,5
发表期刊	IEEE TRANSACTIONS ON CYBERNETICS
	2013-02-01
卷号	43 期号:1 页码:51-63
文章类型	Article
摘要	Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the first time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.
关键词	Data Mining Machine Learning Manifold Learning Nonlinear Dimensionality Reduction (Ndr)
WOS标题词	Science & Technology ; Technology
关键词[WOS]	NEIGHBORHOOD PRESERVING PROJECTIONS ; DIMENSIONALITY REDUCTION ; GEOMETRIC FRAMEWORK ; FACE RECOGNITION ; DYNAMIC SHAPE ; LAPLACIANFACES ; EXTRAPOLATION ; EIGENMAPS ; ALIGNMENT ; EXAMPLES
收录类别	SCI
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Cybernetics
WOS记录号	WOS:000317643500005
引用统计	被引频次：68[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/3029
专题	多模态人工智能系统全国重点实验室_机器人理论与应用
作者单位	1.Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China 2.Natl Disaster Reduct Ctr China, Ctr Data, Beijing 100124, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 5.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
第一作者单位	中国科学院自动化研究所
推荐引用方式 GB/T 7714	Qiao, Hong,Zhang, Peng,Wang, Di,et al. An Explicit Nonlinear Mapping for Manifold Learning[J]. IEEE TRANSACTIONS ON CYBERNETICS,2013,43(1):51-63.
APA	Qiao, Hong,Zhang, Peng,Wang, Di,&Zhang, Bo.(2013).An Explicit Nonlinear Mapping for Manifold Learning.IEEE TRANSACTIONS ON CYBERNETICS,43(1),51-63.
MLA	Qiao, Hong,et al."An Explicit Nonlinear Mapping for Manifold Learning".IEEE TRANSACTIONS ON CYBERNETICS 43.1(2013):51-63.