The analytical solution of gamma filter model

Author

Chiang, Tai-Wu

Author_Institution

Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Volume

2

fYear

1997

fDate

9-12 Jun 1997

Firstpage

685

Abstract

Gamma filter has been proposed by De Vries and Principe (1992) as a functional approximator. In order to get the (sub) optimal values of weights and (temporal resolution) μ, numerical training algorithms have been derived by Lawrence et al. (1996) and Principe et al. (1994). This paper presents an analytical approach to this optimization problem. Using the classical Laguerre polynomial, we have successfully uncoupled and derived the optimal exact solutions for the weights and μ. Finally, we have a geometrical interpretation of the whole idea as an inner product preserved transformation between linear vector spaces

Keywords

function approximation; minimisation; neural nets; polynomials; signal processing; classical Laguerre polynomial; functional approximator; gamma filter model; inner product preserved transformation; linear vector spaces; numerical training algorithms; optimal exact solutions; optimization problem; temporal resolution; Convolution; Electronic mail; Equations; Filters; Kernel; Neural networks; Neurons; Polynomials; Signal processing; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks,1997., International Conference on

Conference_Location

Houston, TX

Print_ISBN

0-7803-4122-8

Type

conf

DOI

10.1109/ICNN.1997.616104

Filename

616104