多类单输入多项式神经网络预测能力比较  

Comparison on Prediction Abilities of Single-Input Neuronets Activated by Different Polynomials

作　　者：张雨浓[1] 陈锦浩[1] 劳稳超[1] 张智军[1] 仇尧 

机构地区：[1]中山大学信息科学与技术学院,广州510006

出　　处：《系统仿真学报》2014年第1期90-96,共7页Journal of System Simulation

基　　金：国家自然科学基金(61075121);教育部高等学校博士学科点专项科研基金博导类课题(20100171110045)

摘　　要：多项式神经网络是根据函数逼近理论与多项式插值建立的一种以线性无关或者正交多项式为隐层神经元激励函数的前向神经网络。分别利用Legendre多项式、Hermite多项式、第一类Chebyshev多项式、第二类Chebyshev多项式、Bernoulli多项式及幂函数构造相应的单输入多项式神经网络,设计出一种适用于该六类神经网络的增长型权值与结构确定算法以确定其相应的最优网络结构与连接权值。基于该算法,深入研究了采用不同的隐层神经元激励函数时多项式神经网络的学习和预测能力。仿真结果表明,除了由Hermite多项式和Bernoulli多项式构建的神经网络的学习和预测能力相对一般外,其他四类神经网络都具有较为优越的学习和预测能力。最后,利用第一类Chebyshev多项式神经网络对世界人口趋势进行了仿真预测。Based on the theory of function approximation and polynomial interpolation, polynomial neuronets are constructed by using linearly independent or orthogonal polynomials as activation functions of hidden-layer neurons. After using Legendre polynomials, Hermite polynomials, Chebyshev polynomials of class I, Chebyshev polynomials of class II, Bernoulli polynomials and power.functions as activation .functions to construct single-input neuronets, a weights-and-structure-determination algorithm of growing type is proposed, which can be applied to these six aforementioned neuronets to determine the optimal structure and weights. With this algorithm, the abilities of learning and prediction of these six neuronets activated by different polynomials are further investigated. Simulation results show that, though the Hermite polynomial neuronet and the Bernoulli polynomial neuronet perform relatively ordinarily, other four neuronets possess superior abilities of learning and prediction. Finally, the neuronet using Chebyshev polynomials of class I is used to simulate the trend of the world population.

关 键 词：单输入多项式神经网络 权值与结构确定算法 预测 线性无关多项式 正交多项式 世界人口 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]