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  Statistical Properties of Kernel Principal Component Analysis

Blanchard, G., Bousquet, O., & Zwald, L. (2006). Statistical Properties of Kernel Principal Component Analysis. Machine Learning, 66(2-3), 259-294. doi:10.1007/s10994-006-6895-9.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D273-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-95FA-A
Genre: Journal Article

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Blanchard, G, Author
Bousquet, O1, Author              
Zwald, L, Author
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1External Organizations, ou_persistent22              

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 Abstract: We study the properties of the eigenvalues of Gram matrices in a non-asymptotic setting. Using local Rademacher averages, we provide data-dependent and tight bounds for their convergence towards eigenvalues of the corresponding kernel operator. We perform these computations in a functional analytic framework which allows to deal implicitly with reproducing kernel Hilbert spaces of infinite dimension. This can have applications to various kernel algorithms, such as Support Vector Machines (SVM). We focus on Kernel Principal Component Analysis (KPCA) and, using such techniques, we obtain sharp excess risk bounds for the reconstruction error. In these bounds, the dependence on the decay of the spectrum and on the closeness of successive eigenvalues is made explicit.

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 Dates: 2006-03
 Publication Status: Published in print
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 Identifiers: DOI: 10.1007/s10994-006-6895-9
BibTex Citekey: 2592
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Title: Machine Learning
Source Genre: Journal
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Publ. Info: Dordrecht : Springer
Pages: - Volume / Issue: 66 (2-3) Sequence Number: - Start / End Page: 259 - 294 Identifier: ISSN: 0885-6125
CoNE: https://pure.mpg.de/cone/journals/resource/08856125