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Methods of representation for kernel canonical correlation analysis

Author

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  • Łukasz Waszak
  • Mirosław Krzyśko

Abstract

Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation. This problem is equivalent to solving the generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we construct nonlinear canonical correlation analysis in reproducing kernel Hilbert spaces. The new kernel generalized eigenvalue problem always has the solution equal to one, and this is a typical case of over-fitting. We present methods to solve this problem and compare the results obtained by classical and kernel canonical correlation analysis.

Suggested Citation

  • Łukasz Waszak & Mirosław Krzyśko, 2012. "Methods of representation for kernel canonical correlation analysis," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(2), pages 301-310, June.
    • Handle: RePEc:csb:stintr:v:13:y:2012:i:2:p:301-310
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