On the convergence of eigenspaces in Kernel principal component analysis

Advances in Neural Information Processing Systems

Volumn , Issue , 2005, Pages 1649-1656

  Zwald, Laurent ^a   Blanchard, Gilles ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b FRAUNHOFER FIRST   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ERRORS; EIGENSPACES; EIGENVALUES; KERNEL PRINCIPAL COMPONENT ANALYSES (KPCA); NON-ASYMPTOTIC; RECONSTRUCTION ERROR; STABILITY RESULTS; UPPER BOUND;

EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 84864041215     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. R. Bhatia and L. Elsner. The Hoffman-Wielandt inequality in infinite dimensions. Proc.Indian Acad.Sci(Math. Sci.) 104 (3), p. 483-494, 1994.
2. G. Blanchard, O. Bousquet, and L. Zwald. Statistical Properties of Kernel Principal Component Analysis. Proceedings of the 17th. Conference on Learning Theory (COLT 2004), p. 594-608. Springer, 2004.
3. G. Blanchard, P. Massart, R. Vert, and L. Zwald. Kernel projection machine: a new tool for pattern recognition. Proceedings of the 18th. Neural Information Processing System (NIPS 2004), p. 1649-1656. MIT Press, 2004.
4. J. Dauxois, A. Pousse, and Y. Romain. Asymptotic theory for the Principal Component Analysis of a vector random function: some applications to statistical inference. Journal of multivariate analysis 12, 136-154, 1982.
5. T. Kato. Perturbation Theory for Linear Operators. New-York: Springer-Verlag, 1966.
6. V. Koltchinskii. Asymptotics of spectral projections of some random matrices approximating integral operators. Progress in Probability, 43:191-227, 1998.
7. V. Koltchinskii and E. Giné. Random matrix approximation of spectra of integral operators. Bernoulli, 6(1):113-167, 2000.
8. B. Schölkopf, A. J. Smola, and K.-R. Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998.
9. J. Shawe-Taylor and N. Cristianini. Estimating the moments of a random vector with applications. Proceedings of the GRETSI 2003 Conference, p. 47-52, 2003.
10. J. Shawe-Taylor, C. Williams, N. Cristianini, and J. Kandola. On the eigenspectrum of the Gram matrix and the generalisation error of Kernel PCA. IEEE Transactions on Information Theory 51 (7), p. 2510-2522, 2005.
11. U. von Luxburg, M. Belkin, and O. Bousquet. Consistency of spectral clustering. Technical Report 134, Max Planck Institute for Biological Cybernetics, 2004.
12. U. von Luxburg, O. Bousquet, and M. Belkin. On the convergence of spectral clustering on random samples: the normalized case. Proceedings of the 17th Annual Conference on Learning Theory (COLT 2004), p. 457-471. Springer, 2004.
13. C. K. I. Williams and M. Seeger. The effect of the input density distribution on kernel-based classifiers. Proceedings of the 17th International Conference on Machine Learning (ICML), p. 1159-1166. Morgan Kaufmann, 2000.