An Explicit Nonlinear Mapping for Manifold Learning

CORC > 自动化研究所 > 中国科学院自动化研究所 > 复杂系统管理与控制国家重点实验室 > 机器人应用与理论组

	An Explicit Nonlinear Mapping for Manifold Learning
	Qiao, Hong1 ; Zhang, Peng 2; Wang, Di 3,4; Zhang, Bo 4,5
刊名	IEEE TRANSACTIONS ON CYBERNETICS
	2013-02-01
卷号	43 期号:1 页码:51-63
关键词	Data mining machine learning manifold learning nonlinear dimensionality reduction (NDR)
英文摘要	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.
WOS标题词	Science & Technology ; Technology
类目[WOS]	Computer Science, Artificial Intelligence ; Computer Science, Cybernetics
研究领域[WOS]	Computer Science
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记录号	WOS:000317643500005
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/3029]
专题	自动化研究所_复杂系统管理与控制国家重点实验室_机器人应用与理论组
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
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.