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On the Eigenspectrum of the Gram matrix and the generalisation error of kernel PCA

On the Eigenspectrum of the Gram matrix and the generalisation error of kernel PCA
On the Eigenspectrum of the Gram matrix and the generalisation error of kernel PCA
In this paper we analyze the relationships between the eigenvalues of the m x m Gram matrix K for a kernel k(.,.) corresponding to a sample x1,...,xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA showing that we can expect good performance even in very high dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.
0018-9448
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Williams, Chris
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Cristianini, Nello
091768cb-dfc6-4422-827d-f520fefc4b40
Kandola, Jaz
a3e03d64-c32c-45ba-aaca-098f9cad1570
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Williams, Chris
7ddfbfec-6be6-40ca-9bd7-e4a4bf288781
Cristianini, Nello
091768cb-dfc6-4422-827d-f520fefc4b40
Kandola, Jaz
a3e03d64-c32c-45ba-aaca-098f9cad1570

Shawe-Taylor, John, Williams, Chris, Cristianini, Nello and Kandola, Jaz (2004) On the Eigenspectrum of the Gram matrix and the generalisation error of kernel PCA. IEEE Transactions on Information Theory, 51.

Record type: Article

Abstract

In this paper we analyze the relationships between the eigenvalues of the m x m Gram matrix K for a kernel k(.,.) corresponding to a sample x1,...,xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA showing that we can expect good performance even in very high dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.

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Published date: 2004
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 259779
URI: http://eprints.soton.ac.uk/id/eprint/259779
ISSN: 0018-9448
PURE UUID: b46cb065-d3fb-415e-b2f4-b4f849a65f39

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Date deposited: 02 Mar 2005
Last modified: 23 Sep 2020 16:34

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Contributors

Author: John Shawe-Taylor
Author: Chris Williams
Author: Nello Cristianini
Author: Jaz Kandola

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