Radial basis function neural networks have superlinear VC dimension

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

Volumn 2111, Issue , 2001, Pages 14-30

  Schmitt, Michael ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; FUNCTIONS; MULTILAYER NEURAL NETWORKS; NEURONS; NUMBER THEORY;

COMPUTATIONAL POWER; INPUT DIMENSIONS; LEARNING CAPABILITIES; NEURAL NETWORKS WITH ONE HIDDEN LAYER; RADIAL BASIS FUNCTION NEURAL NETWORKS; RADIAL BASIS FUNCTION(RBF); SIGMOIDAL NEURAL NETWORKS; VAPNIK-CHERVONENKIS DIMENSIONS;

RADIAL BASIS FUNCTION NETWORKS;

EID: 79952756175     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44581-1_2     Document Type: Conference Paper

References (23)

1. Martin Anthony and Peter L. Bartlett. Neural Network Learning: Theoretical Foundations. Cambridge University Press, Cambridge, 1999.
2. Martin Anthony and Sean B. Holden. Quantifying generalization in linearly weighted neural networks. Complex Systems, 8:91–114, 1994.
3. Peter L. Bartlett, Vitaly Maiorov, and Ron Meir. Almost linear VC dimension bounds for piecewise polynomial networks. Neural Computation, 10:2159–2173, 1998.
4. Christopher M. Bishop. Neural Networks for Pattern Recognition. Clarendon Press, Oxford, 1995.
5. D. S. Broomhead and David Lowe. Multivariable functional interpolation and adaptive networks. Complex Systems, 2:321–355, 1988.
6. Thomas M. Cover. Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Transactions on Electronic Computers, 14:326–334, 1965.
7. Yossi Erlich, Dan Chazan, Scott Petrack, and Avraham Levy. Lower bound on VC-dimension by local shattering. Neural Computation, 9:771–776, 1997.
8. Vadim D. Glezer: Vision and Mind: Modeling Mental Functions. Lawrence Erlbaum, Mahwah, New Jersey, 1995.
9. Eric J. Hartman, James D. Keeler, and Jacek M. Kowalski. Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation, 2:210–215, 1990.
10. Pascal Koiran and Eduardo D. Sontag. Neural networks with quadratic VC dimension. Journal of Computer and System Sciences, 54:190–198, 1997.
11. Wee Sun Lee, Peter L. Bartlett, and Robert C. Williamson. Lower bounds on the VC dimension of smoothly parameterized function classes. Neural Computation, 7:1040–1053, 1995.
12. Wee Sun Lee, Peter L. Bartlett, and Robert C. Williamson. Correction to “Lower bounds on VC-dimension of smoothly parameterized function classes”. Neural Computation, 9:765–769, 1997.
13. Wolfgang Maass. Neural nets with super-linear VC-dimension. Neural Computation, 6:877–884, 1994.
14. David Marr. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. Freeman, New York, 1982.
15. H. N. Mhaskar. Neural networks for optimal approximation of smooth and analytic functions. Neural Computation, 8:164–177, 1996.
16. John Moody and Christian J. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1:281–294, 1989.
17. John G. Nicholls, A. Robert Martin, and Bruce G. Wallace. From Neuron to Brain: A Cellular and Molecular Approach to the Function of the Nervous System. Sinauer Associates, Sunderland, Mass., third edition, 1992.
18. Jooyoung Park and Irwin W. Sandberg. Approximation and radial-basis-function networks. Neural Computation, 5:305–316, 1993.
19. Tomaso Poggio and Federico Girosi. Networks for approximation and learning. Proceedings of the IEEE, 78:1481–1497, 1990.
20. M. J. D. Powell. The theory of radial basis function approximation in 1990. In Will Light, editor, Advances in Numerical Analysis II: Wavelets, Subdivision Algorithms, and Radial Basis Functions, chapter 3, pages 105–210. Clarendon Press, Oxford, 1992.
21. B. D. Ripley. Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge, 1996.
22. Akito Sakurai. Tighter bounds of the VC-dimension of three layer networks. In Proceedings of the World Congress on Neural Networks, volume 3, pages 540–543. Erlbaum, Hillsdale, New Jersey, 1993.
23. Marc Tessier-Lavigne. Phototransduction and information processing in the retina. In Eric R. Kandel, James H. Schwartz, and Thomas M. Jessell, editors, Principles of Neural Science, chapter 28, pages 400–418. Prentice Hall, Englewood Cliffs, New Jersey, third edition, 1991.