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Matrix optimization based Euclidean embedding with outliers

Author

Listed:
  • Qian Zhang

    (Beijing University of Technology)

  • Xinyuan Zhao

    (Beijing University of Technology)

  • Chao Ding

    (Chinese Academy of Sciences)

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.

Suggested Citation

  • Qian Zhang & Xinyuan Zhao & Chao Ding, 2021. "Matrix optimization based Euclidean embedding with outliers," Computational Optimization and Applications, Springer, vol. 79(2), pages 235-271, June.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:2:d:10.1007_s10589-021-00279-2
    DOI: 10.1007/s10589-021-00279-2
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    References listed on IDEAS

    as
    1. Chao Ding & Hou-Duo Qi, 2017. "Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation," Computational Optimization and Applications, Springer, vol. 66(1), pages 187-218, January.
    2. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    3. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
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