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Matrix optimization based Euclidean embedding with outliers

文献类型：期刊论文

作者Zhang, Qian2; Zhao, Xinyuan2; Ding, Chao1
刊名COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
出版日期2021-06-01
卷号79期号:2页码:235-271
关键词Euclidean embedding Outliers Matrix optimizationg Low-rank matrix Error bound
ISSN号0926-6003
DOI10.1007/s10589-021-00279-2
英文摘要Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this paper, we propose a matrix optimization based embedding model that can produce reliable embeddings and identify the outliers jointly. We show that the estimators obtained by the proposed method satisfy a non-asymptotic risk bound, implying that the model provides a high accuracy estimator with high probability when the order of the sample size is roughly the degree of freedom up to a logarithmic factor. Moreover, we show that under some mild conditions, the proposed model also can identify the outliers without any prior information with high probability. Finally, numerical experiments demonstrate that the matrix optimization-based model can produce configurations of high quality and successfully identify outliers even for large networks.
资助项目National Natural Science Foundation of China[12071464] ; National Natural Science Foundation of China[11671387] ; National Natural Science Foundation of China[11531014] ; National Natural Science Foundation of China[11688101] ; General Program of Science and Technology of Beijing Municipal Education Commission[KM201810005004] ; Beijing Natural Science Foundation[Z190002]
WOS研究方向Operations Research & Management Science ; Mathematics
语种英语
WOS记录号WOS:000645176600001
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58593]  
专题应用数学研究所
通讯作者Ding, Chao
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China
2.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Zhang, Qian,Zhao, Xinyuan,Ding, Chao. Matrix optimization based Euclidean embedding with outliers[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2021,79(2):235-271.
APA Zhang, Qian,Zhao, Xinyuan,&Ding, Chao.(2021).Matrix optimization based Euclidean embedding with outliers.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,79(2),235-271.
MLA Zhang, Qian,et al."Matrix optimization based Euclidean embedding with outliers".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 79.2(2021):235-271.

入库方式： OAI收割

来源：数学与系统科学研究院

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