Please wait a minute...
浙江大学学报(工学版)
J4  2010, Vol. 44 Issue (2): 271-275    DOI: 10.3785/j.issn.1008-973X.2010.02.011
    
Number determination of hidden-layer nodes for Hermite feed-forward neural network
ZHANG Yu-nong1, XIAO Xiu-chun1, CHEN Yang-wen2, ZOU A-jin1
(1. Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, China;
2. School of Software, Sun Yat-Sen University, Guangzhou 510275, China)
Download:   PDF(0KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

A new feed-forward neural network was constructed by using Hermite orthogonal polynomial as activation function, which originated from the function-approximation theory. All neural bias and weights from input to hidden layer were respectively fixed to be 0 and 1 with approximation capability guaranteed, and a pseudo-inverse based direct-determination method was derived for the optimal neural weights from hidden layer to output layer. Then an order-increasing automatic-determination algorithm was presented for the optimal number of hidden-layer neurons according to the precision requirement. Computer simulation and prediction results based on multiple target-functions show that the proposed algorithms can quickly obtain the optimal number and weights of hidden-layer neurons and have a relatively good prediction capability.

Published: 09 March 2010
CLC:  TP 241  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Cite this article:

ZHANG Yu-Nong, XIAO Xiu-Chun, CHEN Yang-Wen, et al. Number determination of hidden-layer nodes for Hermite feed-forward neural network. J4, 2010, 44(2): 271-275.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2010.02.011     OR     http://www.zjujournals.com/eng/Y2010/V44/I2/271


Hermite前向神经网络隐节点数目自动确定

从函数逼近论出发,构造了一类以Hermite正交基为激励函数的前向神经网络.在保证网络逼近能力的前提下,令其输入层至隐层的权值和各神经元阈值分别为1和0,导出了基于伪逆的隐层至输出层最优权值的直接计算公式.并针对Hermite前向神经网络,提出一种依照学习精度要求而逐次递增型的隐节点数自动、快速、准确的确定算法.对多个目标函数的计算机仿真和预测结果表明,该神经网络权值直接确定方法和隐节点数自动确定算法能很快地找到最优的隐节点数及其对应的最优权值,且网络具有较好的预测能力.

［1］  ZHANG Yu-nong, WANG Jun. Recurrent neural networks for nonlinear output regulation ［J］. Automatica, 2001, 37(8): 11611173.
［2］ ZHANG Yu-nong, WANG Jun. Obstacle avoidance of kinematically redundant manipulators using a dual neural network ［J］. IEEE Transactions on Systems, Man, and Cybernetics, 2004, 34(1): 752759.
［3］ ZHANG Yu-nong, GE Shu-zhi, LEE Tong-heng. A unified quadratic programming based dynamical system approach to joint torque optimization of physically constrained redundant manipulators ［J］. IEEE Transactions on Systems, Man and Cybernetics, 2004, 34(5): 21262132.［4］ ZHANG Yu-nong, JIANG Dan-chi, WANG Jun. A recurrent neural network for solving sylvester equation with time-varying coefficients ［J］. IEEE Transactions on Neural Networks, 2002, 13(5): 10531063.
［5］ ZHANG Yu-nong, GE Shu-zhi. Design and analysis of a general recurrent neural network model for time-varying matrix inversion ［J］. IEEE Transactions on Neural Networks, 2005, 16(6): 14771490.
［6］ 张泉灵,王树青.基于神经网络的非线性预测函数控制［J］.浙江大学学报:工学版,2001,35(5):497501.
ZHANG Quan-ling, WANG Shu-qing. Nonlinear predictive functional control based on a neural network ［J］. Journal of Zhejiang University: Engineering Science, 2001, 35(5): 497501.
［7］ 林成森.数值分析［M］.北京:科学出版社,2007.
［8］ 莫国端,刘开第.函数逼近论方法［M］.北京:科学出版社,2003:113116.
［9］ 陆系群,余英林.前馈神经网络隐层节点的动态删除法［J］.控制理论与应用,1997,14(1):101104.
LU Xi-qun, YU Ying-lin. A method of dynamic pruning the hidden layer nodes in a feedforward neural network ［J］. Control Theory and Application, 1997, 14(1): 101104.
［10］ 赵启林,陈斌,卓家寿.前馈神经网络结构自删除算法的研究［J］.河海大学学报,2000,28(4):6366.
ZHAO Qi-lin, CHEN Bin, ZHUO Jia-shou. Self-dele-ting algorithm of feedforward neural networks ［J］. Journal of HoHai University, 2000, 28(4): 6366.
［11］ 王上飞,汤汇道.自适应径向基函数神经网络［J］.合肥工业大学学报：自然科学版,2001,24(2):244247.
WANG Shang-fei, TANG Hui-dao. Adaptive radial basis function neural network ［J］. Journal of Hefei University of Technology： Natural Science Edition, 2001, 24(2): 244247.
［12］ 吴建昱,何小荣.用于ANN训练的OBD剪枝算法的改进［J］.化工学报,2002,53(11):11061110.
WU Jian-yu, HE Xiao-rong. Improvement of OBD pruning algorithm for ANN training ［J］. Journal of Chemical Industry and Engineering, 2002, 53(11): 1106 1110.
［13］ 李玉鉴.前馈神经网络中隐层神经元数目的一种直接估计法［J］.计算机学报,1999,22(11):12041208.
LI Yu-jian. A method to directly estimate the number of the hidden neurons in the feedforward neural networks ［J］. Chinese Journal of Computers, 1999, 22(11): 12041208.
［14］ 张雨浓,李巍,刘巍,等.幂激励前向神经网络的权值直接确定法［C］//第1届全国模式识别学术会议.北京：科学出版社,2007:7277.
ZHANG Yu-nong, LI Wei, LIU Wei, et al. Power-activation feed-forward neural network with its weights immediately determined ［C］//The 1st Chinese Conference on Pattern Recognition. Beijing: Science Press, 2007: 7277.
[1] NI Chu-feng, LIU Shan. Adaptive preshaping vibration control for load-varying
flexible manipulator[J]. J4, 2012, 46(8): 1520-1525.
[2] JIN Bo, LIU Shan. Iterative learning control based on terminal endpoint tracking error of
flexible manipulator[J]. J4, 2012, 46(8): 1512-1519.
[3] ZHONG Cong-wei, XIANG Ji, WEI Wei, ZHANG Yuan-hui, CHEN Peng. Collision detection and safe reaction of manipulator
based on disturbance observer[J]. J4, 2012, 46(6): 1115-1121.
[4] ZHONG Cong-wei, XIANG Ji, WEI Wei, ZHANG Yuan-hui. Simple nonlinear observer based dynamic LuGre friction compensation[J]. J4, 2012, 46(4): 764-769.
[5] JIANG Hong-Chao, LIU Shi-Rong, ZHANG Bei-Chao. Inverse kinematics analysis for 6 degree-of-freedom modular
manipulator[J]. J4, 2010, 44(7): 1348-1354.
[6] SHUAI Xin, LI Yan-Jun, TUN Tie-Jun. Real time predictive control algorithm for endpoint trajectory tracking of flexible manipulator[J]. J4, 2010, 44(2): 259-264.