Maximal Linear Embedding for Dimensionality Reduction

doi:10.1109/TPAMI.2011.39

	Maximal Linear Embedding for Dimensionality Reduction
	Wang, Ruiping 1; Shan, Shiguang 2; Chen, Xilin 2; Chen, Jie 3; Gao, Wen 4
	2011-09-01
发表期刊	IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
ISSN	0162-8828
卷号	33 期号:9 页码:1776-1792
摘要	Over the past few decades, dimensionality reduction has been widely exploited in computer vision and pattern analysis. This paper proposes a simple but effective nonlinear dimensionality reduction algorithm, named Maximal Linear Embedding (MLE). MLE learns a parametric mapping to recover a single global low-dimensional coordinate space and yields an isometric embedding for the manifold. Inspired by geometric intuition, we introduce a reasonable definition of locally linear patch, Maximal Linear Patch (MLP), which seeks to maximize the local neighborhood in which linearity holds. The input data are first decomposed into a collection of local linear models, each depicting an MLP. These local models are then aligned into a global coordinate space, which is achieved by applying MDS to some randomly selected landmarks. The proposed alignment method, called Landmarks-based Global Alignment (LGA), can efficiently produce a closed-form solution with no risk of local optima. It just involves some small-scale eigenvalue problems, while most previous aligning techniques employ time-consuming iterative optimization. Compared with traditional methods such as ISOMAP and LLE, our MLE yields an explicit modeling of the intrinsic variation modes of the observation data. Extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm.
关键词	Dimensionality reduction manifold learning maximal linear patch landmarks-based global alignment
DOI	10.1109/TPAMI.2011.39
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of China[61025010] ; Natural Science Foundation of China[60872077] ; National Basic Research Program of China (973 Program)[2009CB320902]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS记录号	WOS:000292740000006
出版者	IEEE COMPUTER SOC
引用统计	被引频次：53[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/13076
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Wang, Ruiping
作者单位	1.Tsinghua Univ, Dept Automat, Broadband Network & Multimedia Lab, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Inst Comp Technol, Key Lab Intelligent Informat Proc, Beijing 100190, Peoples R China 3.Univ Oulu, Dept Elect & Informat Engn, Machine Vis Grp, FI-90014 Oulu, Finland 4.Peking Univ, Sch EECS, Key Lab Machine Percept MoE, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Wang, Ruiping,Shan, Shiguang,Chen, Xilin,et al. Maximal Linear Embedding for Dimensionality Reduction[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2011,33(9):1776-1792.
APA	Wang, Ruiping,Shan, Shiguang,Chen, Xilin,Chen, Jie,&Gao, Wen.(2011).Maximal Linear Embedding for Dimensionality Reduction.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,33(9),1776-1792.
MLA	Wang, Ruiping,et al."Maximal Linear Embedding for Dimensionality Reduction".IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 33.9(2011):1776-1792.