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Statistical Consistency of Kernel Canonical Correlation Analysis

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83923

Fukumizu,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Fukumizu, K., Bach, F., & Gretton, A. (2007). Statistical Consistency of Kernel Canonical Correlation Analysis. Journal of Machine Learning Research, 8, 361-383. Retrieved from http://jmlr.csail.mit.edu/papers/volume8/fukumizu07a/fukumizu07a.pdf.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-CEAF-D
Zusammenfassung
While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not yet been established. This paper gives a mathematical proof of the statistical convergence of kernel CCA, providing a theoretical justification for the method. The proof uses covariance operators defined on reproducing kernel Hilbert spaces, and analyzes the convergence of their empirical estimates of finite rank to their population counterparts, which can have infinite rank. The result also gives a sufficient condition for convergence on the regularization coefficient involved in kernel CCA: this should decrease as n^-1/3, where n is the number of data.