Boundedness of the nominal coefficients in Gaussian RBF neural networks

被引:6
作者
Ignacio Mulero-Martinez, Juan [1 ]
机构
[1] Univ Politecn Cartagena, Dept Ingn Sistemas & Automat, Cartagena 30203, Spain
关键词
best approximation; truncation errors; sampling theory; radial basis functions; bandlimited functions; existence and uniqueness; curse of dimensionality;
D O I
10.1016/j.neucom.2007.01.011
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The paper analyzes the boundedness of the coefficients involved in Gaussian expansion series. These series arise from the reconstruction of bandlimited functions, applying the sampling theorem with Gaussians as reconstruction filters. The boundedness of the ideal coefficients is a previous requirement that should be imposed to the approximation function. This is due to the fact that the coefficient sequence should be absolutely summable. With this sort of requirements, the targeted function is guaranteed to exhibit finite energy so that it will be manageable from the viewpoint of the approximation theory. On the other hand, the bounds of the coefficients affect considerably to the approximation errors and consequently to the accuracy of the estimation. The major result of this work is formalized in a series of propositions where it is stated how the coefficients are upper bounded by a signal "sinus cardinalis" (sinc). Finally, an energy measure of the approximation error is determined as a mean square error. In this line, a number of results are presented in both the univariate and the multivariate case showing how these errors strongly depend on the coefficients in the Gaussian expansion.(c) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:197 / 220
页数:24
相关论文
共 23 条
[1]  
Abramowitz M., 1974, HDB MATH FUNCTIONS F
[2]   FAMILIES OF MULTIRESOLUTION AND WAVELET SPACES WITH OPTIMAL PROPERTIES [J].
ALDROUBI, A ;
UNSER, M .
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1993, 14 (5-6) :417-446
[3]  
[Anonymous], 1998, COMPLEXITY REAL COMP, DOI DOI 10.1007/978-1-4612-0701-6
[4]   ROBUST OUTPUT TRACKING FOR NONLINEAR-SYSTEMS [J].
BEHTASH, S .
INTERNATIONAL JOURNAL OF CONTROL, 1990, 51 (06) :1381-1407
[5]   Issues in the application of neural networks for tracking based on inverse control [J].
Cabrera, JBD ;
Narendra, KS .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (11) :2007-2027
[6]  
DAUBECHIES I, 1998, CBMS NSF REG C SER A, V61
[7]  
Ge S.S., 2002, STABLE ADAPTIVE NEUR
[8]  
GE SS, 1996, IFAC WORLD C SAN FRA, P139
[9]  
GOH CJ, 1994, CONTR-THEOR ADV TECH, V10, P539
[10]   NEURAL NETWORKS FOR CONTROL-SYSTEMS - A SURVEY [J].
HUNT, KJ ;
SBARBARO, D ;
ZBIKOWSKI, R ;
GAWTHROP, PJ .
AUTOMATICA, 1992, 28 (06) :1083-1112