On the capabilities of higher-order neurons: A radial basis function approach

Neural Computation

Volumn 17, Issue 3, 2005, Pages 715-729

  Schmitt, Michael ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; NERVE CELL; PHYSIOLOGY;

ALGORITHMS; ANIMALS; ARTIFICIAL INTELLIGENCE; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS;

EID: 13844298256     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/0899766053019953     Document Type: Article

References (19)

1. Anthony, M., & Bartlett, P. L. (1999). Neural network learning: Theoretical foundations. Cambridge: Cambridge University Press.
2. Bartlett, P. L., & Maass, W. (2003). Vapnik-Chervonenkis dimension of neural nets. In M. A. Arbib (Ed.), The handbook of brain theory and neural networks, (2nd ed., pp. 1188-1192). Cambridge, MA: MIT Press.
3. Bartlett, P. L., Maiorov, V., & Meir, R. (1998). Almost linear VC-dimension bounds for piecewise polynomial networks. Neural Computation, 10, 2159-2173.
4. Ben-David, S., & Lindenbaum, M. (1998). Localization vs. identification of semi-algebraic sets. Machine Learning, 32, 207-224.
5. Durbin, R., & Rumelhart, D. (1989). Product units: A computationally powerful and biologically plausible extension to backpropagation networks. Neural Computation, 1, 133-142.
6. Ehrenfeucht, A., Haussler, D., Kearns, M., & Valiant, L. (1989). A general lower bound on the number of examples needed for learning. Information and Computation, 82, 247-261.
7. Erlich, Y., Chazan, D., Petrack, S., & Levy, A. (1997). Lower bound on VC-dimension by local shattering. Neural Computation, 9, 771-776.
8. Haykin, S. (1999). Neural networks: A comprehensive foundation (2nd ed.). Upper Saddle River, NJ: Prentice Hall.
9. Karpinski, M., & Macintyre, A. (1997). Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks. Journal of Computer and System Sciences, 54, 169-176.
10. Karpinski, M., & Werther, T. (1993). VC dimension and uniform learnability of sparse polynomials and rational functions. SIAM Journal on Computing, 22, 1276-1285.
11. Koiran, P., & Sontag, E. D. (1997). Neural networks with quadratic VC dimension. Journal of Computer and System Sciences, 54, 190-198.
12. Lee, W. S., Bartlett, P. L., & Williamson, R. C. (1995). Lower bounds on the VC dimension of smoothly parameterized function classes. Neural Computation, 7, 1040-1053.
13. Littlestone, N. (1988). Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2, 285-318.
14. Park, J., & Sandberg, I. W. (1991). Universal approximation using radial-basis-function networks. Neural Computation, 3, 246-257.
15. Schmitt, M. (2002a). Descartes' rule of signs for radial basis function neural networks. Neural Computation, 14, 2997-3011.
16. Schmitt, M. (2002b). Neural networks with local receptive fields and superlinear VC dimension. Neural Computation, 14, 919-956.
17. Schmitt, M. (2002c). On the complexity of computing and learning with multiplicative neural networks. Neural Computation, 14, 241-301.
18. Schmitt, M. (2004). New designs for the Descartes rule of signs. American Mathematical Monthly, 111, 159-164.
19. Vapnik, V. N., & Chervonenkis, A. Y. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Its Applications, 16, 264-280.