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Detecting influential observations in Kernel PCA

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  • Debruyne, Michiel
  • Hubert, Mia
  • Van Horebeek, Johan
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    Abstract

    Kernel Principal Component Analysis extends linear PCA from a Euclidean space to any reproducing kernel Hilbert space. Robustness issues for Kernel PCA are studied. The sensitivity of Kernel PCA to individual observations is characterized by calculating the influence function. A robust Kernel PCA method is proposed by incorporating kernels in the Spherical PCA algorithm. Using the scores from Spherical Kernel PCA, a graphical diagnostic is proposed to detect points that are influential for ordinary Kernel PCA.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 12 (December)
    Pages: 3007-3019

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3007-3019

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    Web page: http://www.elsevier.com/locate/csda

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    1. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    2. Marden, John I., 1999. "Some robust estimates of principal components," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 349-359, July.
    3. Hubert, Mia & Rousseeuw, Peter & Verdonck, Tim, 2009. "Robust PCA for skewed data and its outlier map," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2264-2274, April.
    4. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-73, June.
    5. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    6. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
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    Cited by:
    1. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
    2. Heinrich Fritz & Peter Filzmoser & Christophe Croux, 2012. "A comparison of algorithms for the multivariate L 1 -median," Computational Statistics, Springer, vol. 27(3), pages 393-410, September.

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