ML Anthology

On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum

John Shawe-Taylor, Christopher K. I. Williams, Nello Cristianini, Jaz S. Kandola
ALT 2002 pp. 23-40
doi:10.1007/3-540-36169-3_4 /alt/2002/shawetaylor2002alt-eigenspectrum/

Abstract

In this paper we analyze the relationships between the eigenvalues of the m х m Gram matrix K for a kernel k (·, ·) corresponding to a sample x_1, . . . , x^m drawn from a density p (x) and and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA.

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Cite

Text

Shawe-Taylor et al. "On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum." International Conference on Algorithmic Learning Theory, 2002. doi:10.1007/3-540-36169-3_4

Markdown

[Shawe-Taylor et al. "On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum." International Conference on Algorithmic Learning Theory, 2002.](https://mlanthology.org/alt/2002/shawetaylor2002alt-eigenspectrum/) doi:10.1007/3-540-36169-3_4

BibTeX

@inproceedings{shawetaylor2002alt-eigenspectrum,
  title     = {{On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum}},
  author    = {Shawe-Taylor, John and Williams, Christopher K. I. and Cristianini, Nello and Kandola, Jaz S.},
  booktitle = {International Conference on Algorithmic Learning Theory},
  year      = {2002},
  pages     = {23-40},
  doi       = {10.1007/3-540-36169-3_4},
  url       = {https://mlanthology.org/alt/2002/shawetaylor2002alt-eigenspectrum/}
}