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The Equivalence Between Principal Component Analysis and Nearest Flat in the Least Square Sense

Author

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  • Yuan-Hai Shao

    (Zhejiang University of Technology)

  • Nai-Yang Deng

    (China Agricultural University)

Abstract

In this paper, we declare the equivalence between the principal component analysis and the nearest q-flat in the least square sense by showing that, for given m data points, the linear manifold with nearest distance is identical to the linear manifold with largest variance. Furthermore, from this observation, we give a new simpler proof for the approach to find the nearest q-flat.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0647-y
    DOI: 10.1007/s10957-014-0647-y
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    References listed on IDEAS

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    1. Edoardo Amaldi & Kanika Dhyani & Leo Liberti, 2013. "A two-phase heuristic for the bottleneck k-hyperplane clustering problem," Computational Optimization and Applications, Springer, vol. 56(3), pages 619-633, December.
    2. P. Tseng, 2000. "Nearest q-Flat to m Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 249-252, April.
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