Pair-perturbation influence functions and local influence in PCA

Yufen Huang, Mei Ling Kuo, Tai Ho Wang

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The perturbation theory of an eigenvalue problem provides a useful tool for the sensitivity analysis in principal component analysis (PCA). However, single-perturbation diagnostics can suffer from masking effects. In this paper, we develop the pair-perturbation influence functions for the eigenvalues and eigenvectors of covariance matrices utilized in PCA to uncover the masked influential points. The relationship between the empirical pair-perturbation influence function and local influence in pairs is also investigated. Moreover, we propose an approach for determining cut points for influence function values in PCA, which has not been addressed yet. A simulation study and a specific data example are provided to illustrate the application of these approaches.

Original languageEnglish
Pages (from-to)5886-5899
Number of pages14
JournalComputational Statistics and Data Analysis
Volume51
Issue number12
DOIs
Publication statusPublished - 2007 Aug 15

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Local Influence
Influence Function
Principal component analysis
Principal Component Analysis
Perturbation
Eigenvalues and Eigenvectors
Masking
Covariance matrix
Eigenvalues and eigenfunctions
Perturbation Theory
Sensitivity analysis
Eigenvalue Problem
Sensitivity Analysis
Diagnostics
Simulation Study
Influence function
Eigenvalues

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Computational Mathematics
  • Numerical Analysis
  • Statistics and Probability

Cite this

Huang, Yufen ; Kuo, Mei Ling ; Wang, Tai Ho. / Pair-perturbation influence functions and local influence in PCA. In: Computational Statistics and Data Analysis. 2007 ; Vol. 51, No. 12. pp. 5886-5899.
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Pair-perturbation influence functions and local influence in PCA. / Huang, Yufen; Kuo, Mei Ling; Wang, Tai Ho.

In: Computational Statistics and Data Analysis, Vol. 51, No. 12, 15.08.2007, p. 5886-5899.

Research output: Contribution to journalArticle

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