Matrix optimization based Euclidean embedding with outliers

doi:10.1007/s10589-021-00279-2

CSpace > 应用数学研究所

	Matrix optimization based Euclidean embedding with outliers
	Zhang, Qian 1; Zhao, Xinyuan 1; Ding, Chao2
	2021-06-01
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
卷号	79 期号:2 页码:235-271
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.
关键词	Euclidean embedding Outliers Matrix optimizationg Low-rank matrix Error bound
DOI	10.1007/s10589-021-00279-2
收录类别	SCI
语种	英语
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
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000645176600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58594
专题	应用数学研究所
通讯作者	Ding, Chao
作者单位	1.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, 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.