神经网络二阶反向传播学习算法及其收敛性  

Convergence analysis of second order back-propagation learning algorithm for neural network

作　　者：刘铁男[1] 王利国[2] 刘严崴 谢爱华[1] 刘志德[1] 

机构地区：[1]大庆石油学院自动化与控制工程系,黑龙江安达151400 [2]大庆石油管理局供电电器设备有限公司,黑龙江大庆163454 [3]大庆供电公司中心实验所,黑龙江大庆163254

出　　处：《大庆石油学院学报》2001年第4期39-41,共3页Journal of Daqing Petroleum Institute

基　　金：黑龙江省自然科学基金资助项目 (F9812 ) ;黑龙江省教育厅科学技术研究项目 ( 95 5 10 31)

摘　　要：针对BP算法收敛速度慢的问题 ,提出了多层前向神经网络的新型二阶递推学习算法 .给出了一种新的矩阵求逆引理 ,从Newton迭代法入手 ,推导出新型递推学习算法 .该算法等价于Newton迭代法并且有二阶收敛速度 ,能同时反向传播网络各层误差和二阶导数信息因子 ,还能实现Newton搜索方向和Hessian阵逆的递推运算 .基于微分方程稳定性理论 ,研究了新算法的全局收敛性 .分析表明 。In view of the weakness of BP algorithm, a new second order recursive learning algorithm to multilayer feedforward network is proposed. First, a new matrix inversion lemma is given, then using the lemma and from Newton iterative algorithm the new recursive algorithm is deduced. The new algorithm is equivalent to Newton iterative algorithm and has second order convergent speed. It makes not only each layer errors of network but also second order derivative information factors back propagate, and it can achieve the recurrence calculation of Newton search directions and the inverse of Hession matrices. Lastly, based on the theory of differential equation stability the convergence of the new algorithm is reseached. It is proved that the new algorithm is superior to BP algorithm and has global convergence.

关 键 词：全局收敛性 多层前向网络 BP算法 二阶学习算法 Newton算法 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]