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  The Geometry Of Kernel Canonical Correlation Analysis

Kuss, M., & Graepel, T.(2003). The Geometry Of Kernel Canonical Correlation Analysis (108). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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MPIK-TR-108.pdf (Publisher version), 239KB
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Kuss, M1, 2, Author              
Graepel, T, Author
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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: Canonical correlation analysis (CCA) is a classical multivariate method concerned with describing linear dependencies between sets of variables. After a short exposition of the linear sample CCA problem and its analytical solution, the article proceeds with a detailed characterization of its geometry. Projection operators are used to illustrate the relations between canonical vectors and variates. The article then addresses the problem of CCA between spaces spanned by objects mapped into kernel feature spaces. An exact solution for this kernel canonical correlation (KCCA) problem is derived from a geometric point of view. It shows that the expansion coefficients of the canonical vectors in their respective feature space can be found by linear CCA in the basis induced by kernel principal component analysis. The effect of mappings into higher dimensional feature spaces is considered critically since it simplifies the CCA problem in general. Then two regularized variants of KCCA are discussed. Relations to other methods are illustrated, e.g., multicategory kernel Fisher discriminant analysis, kernel principal component regression and possible applications thereof in blind source separation.

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 Dates: 2003-05
 Publication Status: Published in print
 Pages: 11
 Publishing info: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Rev. Type: -
 Identifiers: Report Nr.: 108
BibTex Citekey: 2233
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Title: Technical Report of the Max Planck Institute for Biological Cybernetics
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Pages: - Volume / Issue: 108 Sequence Number: - Start / End Page: - Identifier: -