基于Bernstein多项式的SISO三层前向神经网络的设计与逼近  

Design and approximation of SISO three layers feedforward neural network based on Bernstein polynomials

作　　者：肖炜茗 王贵君[1] XIAO Wei-ming;WANG Gui-jun(School of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《山东大学学报（理学版）》2018年第9期55-61,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61374009)

摘　　要：利用一元Bernstein多项式在相邻等距剖分点的差值和Sigmodial转移函数性质设计单输入单输出(single input single output,SISO)三层前向神经网络,并给出选取连接权和阈值的方法。此外,依据一元Bernstein多项式逼近连续函数定理证明SISO三层前向神经网络对连续函数也具有逼近性,进而通过实例获得该网络的一种输入输出解析表达式。A single input single output（SISO） three layers feedforward neural network was designed by using the difference value between adjacent equidistant subdivision points of unary Bernstein polynomial with a Sigmodial transfer function,and a method of selecting the connection weights and thresholds was given. In addition,according to the approximation theorem for unary Bernstein polynomial,we proved that SISO three layers feedforward neural network could also approximate a continuous function. The analytical expression of the neural network was obtained by an example.

关 键 词：BERNSTEIN多项式 Sigmodial转移函数 等距剖分 前向神经网络 逼近性 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]