Abstract
We present a direct estimation method of the output layer weights in a polynomial extension of the generalized radial-basis-function networks when used in pattern classification problems. The estimation is based on the L2-distance minimization of the density and the population moments. Each synaptic weight in the output layer is derived as a nonlinear function of the training data moments. The experimental results, using one- and two-dimensional simulated data and different polynomial orders, show that the classification rate of the polynomial densities is very close to the optimum rate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bellman, R. Adaptive Control Processes: A Guided Tour. Princeton University Press. (1961)
Dermatas, E.: Polynomial extension of the Generalized Radial-Basis Function Networks in Density estimation and Classification Problems. Neural Network World 10(4) (2000) 553–564
Durbin R., and Rumelhart D.: Product units: A computationally powerful and biologically plausible extension to backpropagation networks. Neural Computation 1 (1989) 133–142
Giles C., and Maxwell T.: Learning, invariance, and generalization in a high-order neural network. Applied Optics 26(23) (1987) 4972–4978
Haykin S.: Neural Networks: A comprehensive foundation. Prendice Hall International Inc. (1999) 298–305
Heywood M., and Noakes P.: A Framework for Improved Training of Sigma-Pi Networks. IEEE Tr. on Neural Networks 6(4) (1995) 893–903
McClelland J., and Rumelhart D.: Parallel Distributed Processing 1. MIT Press (1987)
Poggio T., and Girosi F.: Networks for approximation and learning. Proc. IEEE 78(9) (1990)1481–1497
Shin Y., and Ghosh G.: Ridge Polynomial Networks. IEEE Tr. on Neural Networks 6(3) (1995) 610–622
Pao Y.: Adaptive Pattern Recognition and Neural Networks. Reading MA: Addison-Wesley (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dermatas, E. (2001). Direct Estimation of Polynomial Densities in Generalized RBF Networks Using Moments. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_17
Download citation
DOI: https://doi.org/10.1007/3-540-44668-0_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42486-4
Online ISBN: 978-3-540-44668-2
eBook Packages: Springer Book Archive