Matrix optimization based Euclidean embedding with outliers

Qian Zhang (), Xinyuan Zhao () and Chao Ding ()
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Qian Zhang: Beijing University of Technology
Xinyuan Zhao: Beijing University of Technology
Chao Ding: Chinese Academy of Sciences

Computational Optimization and Applications, 2021, vol. 79, issue 2, No 1, 235-271

Abstract: Abstract 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.

Keywords: Euclidean embedding; Outliers; Matrix optimizationg; Low-rank matrix; Error bound; 49M45; 90C25; 90C33 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-021-00279-2

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