Constructive function-approximation by three-layer artificial neural networks

被引：59

作者：

Suzuki, S ^{[1
]}

机构：

[1] NTT, Basic Res Labs, Informat Sci Res Lab, Atsugi, Kanagawa 2430198, Japan

来源：

NEURAL NETWORKS | 1998年 / 11卷 / 06期

关键词：

three-layer artificial neural network; function approximation; approximating network construction; hidden-layer unit number specification; approximation-error estimation; Jackson's theorem;

D O I：

10.1016/S0893-6080(98)00068-9

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Constructive theorems of three-layer artificial neural networks with (1) trigonometric, (2) piecewise linear, and (3) sigmoidal hidden-layer units are proved in this paper. These networks approximate 2 pi-periodic pth-order Lebesgue-integrable functions (L-2 pi(p)) on R-m to R-n for p greater than or equal to 1 with L-2 pi(p) - norm. (In the case of (1), the networks also approximate 2 pi-periodic continuous functions (C-2 pi) with C-2 pi-norm.) These theorems provide explicit equational representations of these approximating networks, specifications for their numbers of hidden-layer units, and explicit formulations of their approximation-error estimations. The function-approximating networks and the estimations of their approximation errors can practically and easily be calculated from the results. The theorems can easily be applied to the approximation of a nonperiodic function defined in a bounded set on R-m to R-n. (C) 1998 Elsevier Science Ltd. All rights reserved.

引用

页码：1049 / 1058

页数：10