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Matrix optimization based Euclidean embedding with outliers
Zhang, Qian1; Zhao, Xinyuan1; Ding, Chao2
AbstractEuclidean 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.
KeywordEuclidean embedding Outliers Matrix optimizationg Low-rank matrix Error bound
Indexed BySCI
Funding ProjectNational 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 Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000645176600001
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Document Type期刊论文
Corresponding AuthorDing, Chao
Affiliation1.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
Recommended Citation
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.
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