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A correction of approximations used in sensitivity study of principal component analysis

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  • Jacques Bénasséni

    (Univ Rennes, CNRS, IRMAR - UMR 6625)

Abstract

Principal component analysis is a method of dimensionality reduction based on the eigensystem of the covariance matrix of a set of multivariate observations. Analyzing the effects of some specific observations on this eigensystem is therefore of particular importance in the sensitivity study of the results. In this framework, approximations for the perturbed eigenvalues and eigenvectors when deleting one or several observations are useful from a computational standpoint. Indeed, they allow one to evaluate the effects of these observations without having to recompute the exact perturbed eigenvalues and eigenvectors. However, it turns out that some approximations which have been suggested are based on an incorrect application of matrix perturbation theory. The aim of this short note is to provide the correct formulations which are illustrated with a numerical study.

Suggested Citation

  • Jacques Bénasséni, 2018. "A correction of approximations used in sensitivity study of principal component analysis," Computational Statistics, Springer, vol. 33(4), pages 1939-1955, December.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-017-0790-7
    DOI: 10.1007/s00180-017-0790-7
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    References listed on IDEAS

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    1. Prendergast, Luke A. & Li Wai Suen, Connie, 2011. "A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 752-764, January.
    2. Wang, Song-Gui & Nyquist, Hans, 1991. "Effects on the eigenstructure of a data matrix when deleting an observation," Computational Statistics & Data Analysis, Elsevier, vol. 11(2), pages 179-188, March.
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