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  Statistical Consistency of Kernel Canonical Correlation Analysis

Fukumizu, K., Bach, F., & Gretton, A. (2007). Statistical Consistency of Kernel Canonical Correlation Analysis. The Journal of Machine Learning Research, 8, 361-383.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-CEAF-D Version Permalink: http://hdl.handle.net/21.11116/0000-0003-CCBC-4
Genre: Journal Article

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 Creators:
Fukumizu, K, Author              
Bach, FR, Author
Gretton, A1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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 Dates: 2007-02
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 4458
 Degree: -

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Title: The Journal of Machine Learning Research
Source Genre: Journal
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Publ. Info: Cambridge, MA : MIT Press
Pages: - Volume / Issue: 8 Sequence Number: - Start / End Page: 361 - 383 Identifier: ISSN: 1532-4435
CoNE: https://pure.mpg.de/cone/journals/resource/111002212682020_1