Boundedness of Input Space and Effective Dimension of Feature Space in Kernel Methods

IEICE Transactions on Information and Systems

Volumn E87-D, Issue 1, 2004, Pages 258-260

  Ikeda, Kazushi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Effective dimension; Learning theory; Support vector machine

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; POLYNOMIALS; STATISTICAL METHODS; VECTOR QUANTIZATION;

EFFECTIVE DIMENSION; FEATURE SPACE; KERNEL GRAM MATRIC; LEARNING THEORY; SUPPORT VECTOR MACHINE;

LEARNING SYSTEMS;

EID: 0842310256     PISSN: 09168532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. V.N. Vapnik, The Nature of Statistical Learning Theory, Springer-Verlag, New York, 1995.
2. V.N. Vapnik, Statistical Learning Theory, John Wiley & Sons, New York, 1998.
3. M.A. Aizerman, E.M. Braverman, and L.I. Rozonoer, "Theoretical foundations of the potential function method in pattern recognition learning," Automation and Remote Control, vol.25, pp.821-837, 1964.
4. L.G. Valiant, "A theory of the learnable," Commun. ACM, vol.27, pp.1134-1142, 1984.
5. E.B. Baum and D. Haussler, "What size net gives valid generalization?," Neural Comput., vol.1, pp.151-160, 1989.
6. M. Opper and D. Haussler, "Calculation of the learning curve of bayes optimal classification on algorithm for learning a perceptron with noise," Proc. COLT, vol.4, pp.75-87, 1991.
7. S. Amari, N. Fujita, and S. Shinomoto, "Four types of learning curves," Neural Comput., vol.4, pp.605-618, 1992.
8. S. Amari, "A universal theorem on learning curves," Neural Networks, vol.6, pp.161-166, 1993.
9. S. Amari and N. Murata, "Statistical theory of learning curves under entropic loss criterion," Neural Comput., vol.5, pp.140-153, 1993.
10. K. Ikeda and S. Amari, "Geometry of admissible parameter region in neural learning," IEICE Trans. Fundamentals, vol.E79-A, no.6, pp.938-943, June 1996.
11. R. Dietrich, M. Opper, and H. Sompolinsky, "Statistical mechanics of support vector networks," Phys. Rev. Lett., vol.82, no.14, pp.2975-2978, 1999.
12. K. Ikeda, "Input manifold and generalization error in polynomial kernel methods," IEICE Technical Report, NC2002-194, 2003.
13. K. Ikeda, "Geometry and learning curves of kernel methods with polynomial kernels," IEICE Trans. Inf. & Syst. (Japanese Edition), vol.J86-D-II, no.7, pp.918-925, July 2003.
14. K. Ikeda, "Generalization error analysis for polynomial kernel methods - Algebraic geometrical approach," Proc. ICANN, pp.201-208, 2003.
15. B. Schölkopf, S. Mika, C. Burges, P. Knirsch, K.-R. Müller, G. Rätsch, and A.J. Smola, "Input space vs feature space in kernel-based methods," IEEE Trans. Neural Netw., vol.10, no.5, pp.1000-1017, 1999.
16. S.S. Keerthi and C.-J. Lin, "Asymptotic behaviors of support vector machines with Gaussian kernel," Neural Comput., vol.15, pp.1667-1689, 2003.