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Detecting influential observations in Kernel PCA

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

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.

Suggested Citation

  • Debruyne, Michiel & Hubert, Mia & Van Horebeek, Johan, 2010. "Detecting influential observations in Kernel PCA," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3007-3019, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3007-3019
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    1. 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.
    2. 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.
    3. Alam, Md. Ashad & Calhoun, Vince D. & Wang, Yu-Ping, 2018. "Identifying outliers using multiple kernel canonical correlation analysis with application to imaging genetics," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 70-85.
    4. Lan Huong Nguyen & Susan Holmes, 2019. "Ten quick tips for effective dimensionality reduction," PLOS Computational Biology, Public Library of Science, vol. 15(6), pages 1-19, June.

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