Robustness properties of dimensionality reduction with Gaussian random matrices
文献类型:期刊论文
作者 | Han, Bin1; Xu, ZhiQiang2,3 |
刊名 | SCIENCE CHINA-MATHEMATICS |
出版日期 | 2017-10-01 |
卷号 | 60期号:10页码:1753-1778 |
ISSN号 | 1674-7283 |
关键词 | phase retrieval finite frames sparse approximation restricted isometry property Johnson-Lindenstrauss lemma |
DOI | 10.1007/s11425-016-9018-x |
英文摘要 | 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. |
资助项目 | 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研究方向 | Mathematics |
语种 | 英语 |
出版者 | SCIENCE PRESS |
WOS记录号 | WOS:000410823100002 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26581] |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Xu, ZhiQiang |
作者单位 | 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 |
推荐引用方式 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. |
入库方式: OAI收割
来源:数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。