On the Eigenspectrum of the gram matrix and its relationship to the operator Eigenspectrum

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2533, Issue , 2002, Pages 23-40

  Shawe Taylor, John ^a   Williams, Chris ^b   Cristianini, Nello ^c   Kandola, Jaz ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

EIGENPROBLEM; EIGENSPECTRUM; EIGENVALUES; GRAM MATRICES; KERNEL PCA; PERFORMANCE BOUNDS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84942814250     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36169-3_4     Document Type: Conference Paper

References (18)

1. T. W. Anderson. Asymptotic Theory for Principal Component Analysis. Annals of Mathematical Statistics, 34(1):122–148, 1963.
2. M. Anthony and P. Bartlett. Learning in Neural Networks: Theoretical Foundations. Cambridge, England: Cambridge University Press, 1999.
3. C. T. H. Baker. The numerical treatment of integral equations. Clarendon Press, Oxford, 1977.
4. S. Brin and L. Page. The anatomy of a large-scale hypertextual (web) search engine. In Proceedings of the Seventh International World Wide Web Conference, 1998.
5. N. Cristianini and J. Shawe-Taylor. An Introduction to Support Vector Machines. Cambridge University Press, 2000.
6. Nello Cristianini, Huma Lodhi, and John Shawe-Taylor. Latent semantic kernels for feature selection. Technical Report NC-TR-00-080, NeuroCOLT Working Group, http://www.neurocolt.org, 2000.
7. M. L. Eaton and D. E. Tyler. On Wielandt’s Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix. Annals of Statistics, 19(1):260–271, 1991.
8. A. T. James. The distribution of the latent roots of the covariance matrix. Annals of Math. Stat., 31:151–158, 1960.
9. J. Kleinberg. Authoritative sources in a hyperlinked environment. In Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms, 1998.
10. V. Koltchinskii and E. Gine. Random matrix approximation of spectra of integral operators. Bernoulli, 6(1):113–167, 2000.
11. D. N. Lawley. Tests of Significance for the Latent Roots of Covariance and Correlation Matrices. Biometrika, 43(1/2):128–136, 1956.
12. C. McDiarmid. On the method of bounded differences. In Surveys in Combinatorics 1989, pages 148–188. Cambridge University Press, 1989.
13. S. Mika, B. Schölkopf, A. Smola, K.-R. Müller, M. Scholz, and G. Rätsch. Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems 11, 1998.
14. Andrew Y. Ng, Alice X. Zheng, and Michael I. Jordan. Link analysis, eigenvectors and stability. In To appear in the Seventeenth International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.
15. J. Shawe-Taylor, N. Cristianini, and J. Kandola. On the Concentration of Spectral Properties. In T. G. Diettrich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14. MITPress, 2002.
16. C. M. Waternaux. Asymptotic Distribution of the Sample Roots for a Nonnormal Population. Biometrika, 63(3):639–645, 1976.
17. C. K. I. Williams and M. Seeger. The Effect of the Input Density Distribution on Kernel-based Classifiers. In P. Langley, editor, Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000). Morgan Kaufmann, 2000.
18. H. Zhu, C. K. I. Williams, R. J. Rohwer, and M. Morciniec. Gaussian regression and optimal finite dimensional linear models. In C. M. Bishop, editor, Neural Networks and Machine Learning. Springer-Verlag, Berlin, 1998.