No. 1057

Title:

Robust Kernel Principal Component Analysis by Minimum Psi-Principle

Author(s):

Huang, Su-Yun (Institute of Statistical Science, Academia Sinica, Taipei, Taiwan);
Yeh, Yi-Ren (Computer Science and Information Engineering National Taiwan University of Science and Technology, Taipei, Taiwan);
Eguchi, Shinto (Institute of Statistical Mathematics, Tokyo, Japan)

Key words:

functional principal component analysis; influence function; kernel principal component analysis; minimum psi-principle, reproducing kernel Hilbert space; robust statistics; spectrum decomposition

Abstract:

    This article discusses the robustness issue of kernel principal component analysis. A class of new robust procedures is proposed based on the minimum psi principle. The proposed procedures place less weight to outliers and thus behave more resistant to data contamination and model deviation. Theoretical influence functions are derived and numerical examples are presented as well. Both theoretical and numerical results indicate that the psi-based kernel principal component analysis performs more robust than the conventional approach against outliers. Our discussion also applies to functional principal component analysis.