The Modification And Convergence Analysis Of MCA Algorithm

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.