An explicit construction of a reproducing Gaussian kernel Hilbert space

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

Volumn 5, Issue , 2006, Pages

  Xu, Jian Wu ^a   Pokharel, Puskal P ^a   Jeong, Kyu Hwa ^a   Principe, Jose C ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; GAUSSIAN DISTRIBUTION; POLYNOMIALS; THEOREM PROVING;

EIGENDECOMPOSITION; FOCK SPACES; GAUSSIAN KERNEL HILBERT SPACES; REPRODUCING KERNEL HILBERT SPACE (RKHS);

HILBERT SPACES;

EID: 33947710800     PISSN: 15206149     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (11)

1. N. Aronszajn, "Theory of Reproducing Kernels", Trans. of American Mathematical Society, Vol. 68, No. 3, pp. 337-404, May, 1950.
2. F. R. Bach and M. I. Jordan, "Kernel Independent Component Analysis", Journal of Machine Learning Research, Vol. 3, pp. 1-48, 2002.
3. Rui J. P. De Figueiredo, "A Generalized Fock Space Framework for Nonlinear System and Signal Analysis", IEEE Trans. of Circuits and System, Vol. CAS-30, No. 9, pp. 637-647, May, 1983.
4. V. Fock, "Konfigurationsraum und zweite quantelung", Z. Phys., Vol. 75, pp. 622-647, 1932.
5. J. Mercer, "Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations", Philosophical Trans. of Royal Society of London, Series A, Vol. 209, pp. 415-446, 1909.
6. S. Mika, G. Ratsch, J. Weston, B. Scholkopf and K.-R. Muller, "Fisher discriminant analysis with kernels", in Neural Networks for Signal Processing IX, pp. 41-48, New Jersey, 1999.
7. A. Rakotomamonjy and Stephane Canu "Frames, Reproducing Kernels, Regularization and Learning", Journal of Machine Learning Research, Vol.6, pp. 1485-1515, 2005.
8. F. Riesz and B. Sz.-Nagy, Functional Analysis, New York, Ungar, 1955.
9. B. Scholkopf and A. Smola, Learnig with Kernels, MIT Press, 2002.
10. B. Scholkopf, A. Smola and K. -R. Muller "Nonlinear Component Analysis as a Kernel Eigenvalue Problem", Neural Computation Vol. 10, pp. 1299-1319, 1998.
11. V. N. Vapnik, Statistical Learning Theory, New York, Wiley, 1998.