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Nearest q-Flat to m Points

Author

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  • P. Tseng

    (University of Washington)

Abstract

Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ℝn in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0≤q≤n−1.

Suggested Citation

  • P. Tseng, 2000. "Nearest q-Flat to m Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 249-252, April.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:1:d:10.1023_a:1004678431677
    DOI: 10.1023/A:1004678431677
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    Cited by:

    1. Majid Noroozi & Marianna Pensky, 2022. "The Hierarchy of Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 64-107, June.
    2. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.
    3. Renli Liang & Yanqin Bai & Hai Xiang Lin, 2019. "An inexact splitting method for the subspace segmentation from incomplete and noisy observations," Journal of Global Optimization, Springer, vol. 73(2), pages 411-429, February.
    4. Yuan-Hai Shao & Nai-Yang Deng, 2015. "The Equivalence Between Principal Component Analysis and Nearest Flat in the Least Square Sense," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 278-284, July.

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