- Abstract:
-
In this paper the relationships between the eigenvalues of the m x m Gram matrix K for a kernel k(.,.) corresponding to a sample x_1, ..., x_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 PCA is provided showing that good perfromance can be expected even in very high dimensional feature spaces provided that the sample eigenvalues fall sufficiently quickly.
- Links To Paper
- 1st Link
- Bibtex format
- @Misc{EDI-INF-RR-0382,
- author = {
John Shawe-Taylor
and Chris Williams
and Nello Cristianini
and Jaz Kandola
},
- title = {On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel PCA},
- year = 2005,
- volume = {51(7)},
- pages = {2510-2522},
- url = {http://www.dai.ed.ac.uk/homes/ckiw/postscript/gram.pdf},
- }
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