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
相关论文
共 50 条
  • [31] Generalization Performance of Radial Basis Function Networks
    Lei, Yunwen
    Ding, Lixin
    Zhang, Wensheng
    IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2015, 26 (03) : 551 - 564
  • [32] Ensemble with Radial Basis Function Neural Networks for Casablanca Stock Market Returns Prediction
    Lahmiri, Salim
    2014 SECOND WORLD CONFERENCE ON COMPLEX SYSTEMS (WCCS), 2014, : 469 - 474
  • [33] Real time face and mouth recognition using radial basis function neural networks
    Balasubramanian, M.
    Palanivel, S.
    Ramalingam, V.
    EXPERT SYSTEMS WITH APPLICATIONS, 2009, 36 (03) : 6879 - 6888
  • [34] Learning in Deep Radial Basis Function Networks
    Wurzberger, Fabian
    Schwenker, Friedhelm
    ENTROPY, 2024, 26 (05)
  • [35] Face Detection Using Radial Basis Function Neural Networks With Variance Spread Value
    Aziz, Khairul Azha A.
    Ramlee, Ridza Azri
    Abdullah, Shahrum Shah
    Jahari, Ahmad Nizam
    2009 INTERNATIONAL CONFERENCE OF SOFT COMPUTING AND PATTERN RECOGNITION, 2009, : 399 - +
  • [36] Adaptive PID Controller for Active Suspension Using Radial Basis Function Neural Networks
    Zhao, Weipeng
    Gu, Liang
    ACTUATORS, 2023, 12 (12)
  • [37] K-Means Based Radial Basis Function Neural Networks for Rainfall Prediction
    Dubey, Akash Dutt
    2015 INTERNATIONAL CONFERENCE ON TRENDS IN AUTOMATION, COMMUNICATIONS AND COMPUTING TECHNOLOGY (I-TACT-15), 2015,
  • [38] An efficient learning algorithm for improving generalization performance of radial basis function neural networks
    Wang, ZO
    Zhu, T
    NEURAL NETWORKS, 2000, 13 (4-5) : 545 - 553
  • [39] Radial Basis Function Neural Networks for Channel Estimation in MIMO-OFDM Systems
    M. Nuri Seyman
    Necmi Taspinar
    Arabian Journal for Science and Engineering, 2013, 38 : 2173 - 2178
  • [40] An optimized radial basis function neural network with modulation-window activation function
    Lin, Haijun
    Dai, Houde
    Mao, Yihan
    Wang, Lucai
    SOFT COMPUTING, 2024, 28 (05) : 4631 - 4648
12345