Radial basis function neural networks of Hankel translates as universal approximators

被引：1
|
作者：
Marrero, Isabel [1 ]
机构：
[1] Univ La Laguna, Dept Anal Matemat, Aptdo 456, San Cristobal la Laguna 38200, Tenerife, Spain
来源：
ANALYSIS AND APPLICATIONS | 2019年 / 17卷 / 06期
关键词：
Activation function; Hankel translation; nonpolynomiality; radial basis function neural network; universal approximation; NATIVE HILBERT-SPACES; RELAXED CONDITIONS; METRIC-SPACES; RBF NETWORKS; INTERPOLATION; REPRESENTATION; TRANSFORMATION; DISTRIBUTIONS; ERROR;
D O I：
10.1142/S0219530519500064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Radial basis function neural networks (RBFNNs) of Hankel translates of order mu > -1/2 with a continuous activation function sigma for which the limit lim(z -> 0+) z(-mu-1/2)sigma(z) exists are shown to possess the universal approximation property in spaces of continuous and of p-integrable functions, 1 <= p < infinity, on (compact subsets of) [0, infinity) if, and only if, z(-mu-1/2)sigma(z) is not an even polynomial. This extends to the class of RBFNNs under consideration a result already known for RBFNNs of standard translates.
引用
收藏
页码：897 / 930
页数：34
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