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On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA.
- Source :
- IEEE Transactions on Information Theory; Jul2005, Vol. 51 Issue 7, p2510-2522, 13p
- Publication Year :
- 2005
-
Abstract
- In this paper, the relationships between the eigenvalues of the m × m Gram matrix K for a kernel k(.,.) corresponding to a sample x<subscript>1</subscript>,ߪ,x<subscript>m</subscript>, drawn from a density p(x) and the igenvalues 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 51
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 17648427
- Full Text :
- https://doi.org/10.1109/TIT.2005.850052