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Robust Principal Component Analysis Based on Pairwise Correlation Estimators

In: Proceedings of COMPSTAT'2010

Author

Listed:
  • Stefan Van Aelst

    (Ghent University, Dept. of Applied Mathematics and Computer Science)

  • Ellen Vandervieren

    (University of Antwerp, Dept. of Mathematics and Computer Science)

  • Gert Willems

    (Ghent University, Dept. of Applied Mathematics and Computer Science)

Abstract

Principal component analysis tries to explain and simplify the structure of multivariate data. For standardized variables, these principal components correspond to the eigenvectors of their correlation matrix. To obtain a robust principal components analysis, we estimate this correlation matrix componentwise by using robust pairwise correlation estimates. We show that the approach based on pairwise correlation estimators does not need a majority of outlier-free observations which becomes very useful for high dimensional problems. We further demonstrate that the “bivariate trimming” method especially works well in this setting.

Suggested Citation

  • Stefan Van Aelst & Ellen Vandervieren & Gert Willems, 2010. "Robust Principal Component Analysis Based on Pairwise Correlation Estimators," Springer Books, in: Yves Lechevallier & Gilbert Saporta (ed.), Proceedings of COMPSTAT'2010, pages 573-580, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2604-3_59
    DOI: 10.1007/978-3-7908-2604-3_59
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