【作者】 崔强；

【导师】 李正学；

【作者基本信息】 大连理工大学 ， 计算数学， 2009， 硕士

【摘要】 人工神经网络是对人脑的反应机制进行简化、抽象和模拟建立起来的数学模型,通过大量基本组成单位——人工神经元的相互连接而对外界环境输入的信息进行并行分布式的处理,具有较强的自适应性和容错性.作为人工神经网络的一个应用——MCA神经网络学习算法,就是寻找一个方向,使得数据空间在这个方向上的投影有最小的方差.由于其应用的广泛性,MCA算法的收敛性变得非常重要.因为确定离散时间(Deterministic Discrete Time,DDT)系统不要求算法的学习率收敛到零,而且还可以保持算法的离散特征,所以基于DDT系统的MCA收敛性分析是近年来人们研究的热点.本文对Oja-Xu MCA和Ojan MCA学习算法进行了研究.对于前者,我们在归一化Oja-Xu MCA算法的基础上又做了进一步的改进,提出了固定步长的跳步归一化及自适应变步长的跳步归一化方法,提高算法的收敛速度和学习精度,并且还对固定步长的跳步归一化方法做了权值有界性的证明。对于后者,我们在理论上对算法的收敛性进行了分析,将原有学习率的取值范围扩大了一倍,并通过数值试验验证了我们的理论结果。本文的结构安排如下:第一章介绍了人工神经网络及MCA神经网络学习算法的相关背景知识,第二章对归一化Oja-Xu MCA算法进行了改进,第三章对Ojan MCA算法的收敛性做了进一步的研究,最后是结论。更多还原

【Abstract】 Artificial neural network(ANN) is a mathematical model based on the simplification, abstraction and simulation of the reaction system of human brain.ANN deals with information from outside environment in a parallel manner by collection of many basic units called neuron,which ensures the ANN a good quality of self-adaptation and error tolerance. As an application of ANN,MCA neural network learning algorithm,is to search a direction to let the data space have the least variance on the direction.Because of its wide application,the convergence of the MCA algorithm is very important.As the Deterministic Discrete Time (DDT) system doesn’t require the learning rate convert to zero and conserve the discrete of the algorithm,the convergence of MCA algorithm based on DDT is the hotspot of people’s work.This thesis studies the Oja-Xu MCA learning algorithm and the Ojan MCA learning algorithm.To the former,we make some improvements based on the normalizing improvement,put forward the fixed interval normalizing method and adaptive interval normalizing method,which improve the convergence speed and the accuracy.In addition,we prove the boundedness of the fixed interval normalizing method.To the latter,we analysis the convergence of the learning algorithm,and enlarge the scope of the learning rate to twice, which is proved by the numerical experimentation.The structure of this thesis is organized as follows.Chapter 1 gives a brief introduction of ANN and the knowledge of MCA learning algorithm.Chapter 2 makes some improvements based on the normalizing improvement of the Oja-Xu MCA learning algorithm. Chapter 3 is concerned with the further study of the convergence of the Ojan MCA learning algorithm.Finally,a brief conclusion is given.更多还原