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 |
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Hauptverfasser: | , , , |
Format: | Artikel |
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. |
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ISSN: | 0018-9448 1557-9654 |
DOI: | 10.1109/TIT.2005.850052 |