On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA

In this paper, the relationships between the eigenvalues of the m/spl times/m Gram matrix K for a kernel /spl kappa/(/spl middot/,/spl middot/) corresponding to a sample x/sub 1/,...,x/sub m/ drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem is analyzed. The...

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Veröffentlicht in:IEEE transactions on information theory 2005-07, Vol.51 (7), p.2510-2522
Hauptverfasser: Shawe-Taylor, J., Williams, C.K.I., Cristianini, N., Kandola, J.
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Sprache:eng
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Zusammenfassung:In this paper, the relationships between the eigenvalues of the m/spl times/m Gram matrix K for a kernel /spl kappa/(/spl middot/,/spl middot/) corresponding to a sample x/sub 1/,...,x/sub m/ drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem is analyzed. The differences between the two spectra are bounded and a performance bound on kernel principal component analysis (PCA) is provided showing that good performance can be expected even in very-high-dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.850052