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Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization

Author

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  • Li Cui

    (Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China2Beijing Institute of Remote Sensing Information, Beijing 100192, P. R. China)

  • Lu Liu

    (Qian Xuesen Laboratory of Space Technology, No. 104 Youyi Road, Haidian District, Beijing 100094, P. R. China)

  • Di-Rong Chen

    (Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China)

  • Jian-Feng Xie

    (Beijing Institute of Remote Sensing Information, Beijing 100192, P. R. China)

Abstract

In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix X ∈ ℝm×n can be exactly recovered from the linear measurement b = 𝒜(X) ∈ ℝq via some Schatten p0 norm minimization. Moreover it is shown that the explicit bound on exponent p0 in the Schatten p0 norm minimization can be exactly extracted.

Suggested Citation

  • Li Cui & Lu Liu & Di-Rong Chen & Jian-Feng Xie, 2016. "Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-11, February.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:01:n:s0217595916500032
    DOI: 10.1142/S0217595916500032
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    References listed on IDEAS

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    1. Alexander Shapiro, 1982. "Weighted minimum trace factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(3), pages 243-264, September.
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