Robustness properties of dimensionality reduction with Gaussian random matrices

doi:10.1007/s11425-016-9018-x

	Robustness properties of dimensionality reduction with Gaussian random matrices
	Han, Bin 1; Xu, ZhiQiang2,3
	2017-10-01
Source Publication	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
Volume	60 Issue:10 Pages:1753-1778
Abstract	In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property (RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.
Keyword	phase retrieval finite frames sparse approximation restricted isometry property Johnson-Lindenstrauss lemma
DOI	10.1007/s11425-016-9018-x
Language	英语
Funding Project	Natural Sciences and Engineering Research Council of Canada[05865] ; National Natural Science Foundation of China[11422113] ; National Natural Science Foundation of China[91630203] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11331012] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000410823100002
Publisher	SCIENCE PRESS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/26582
Collection	计算数学与科学工程计算研究所
Corresponding Author	Xu, ZhiQiang
Affiliation	1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation GB/T 7714	Han, Bin,Xu, ZhiQiang. Robustness properties of dimensionality reduction with Gaussian random matrices[J]. SCIENCE CHINA-MATHEMATICS,2017,60(10):1753-1778.
APA	Han, Bin,&Xu, ZhiQiang.(2017).Robustness properties of dimensionality reduction with Gaussian random matrices.SCIENCE CHINA-MATHEMATICS,60(10),1753-1778.
MLA	Han, Bin,et al."Robustness properties of dimensionality reduction with Gaussian random matrices".SCIENCE CHINA-MATHEMATICS 60.10(2017):1753-1778.

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