径向基神经网络基函数中心确定方法改进研究

发布时间：2019-04-23 07:47

【摘要】：径向基函数(Radial Basis Function,RBF)神经网络是一种局部逼近的三层前馈型神经网络,相比于其它前馈型神经网络有结构简单、收敛速度快、不会陷入局部最小值点等优点,受到了极大关注并在许多领域得到了广泛应用。在RBF神经网络的构建过程中,运用k-means聚类方法确定基函数中心的学习算法需要预先给出初始聚类中心,当给定的初始聚类中心不同时,得到的基函数中心可能是不同的,导致网络训练结果不稳定,并且网络隐含层神经元的个数需要提前给出,但往往网络结构是不能预先确定的。针对这一问题,提出了运用系统聚类确定基函数中心的方法,从而有效的解决了RBF神经网络对初始聚类中心敏感的问题。本文首先介绍了RBF神经网络的基本原理,对不同RBF神经网络的结构和性能进行了分析,指出各种网络的特点和需要注意的问题。研究了RBF神经网络几种常用的学习算法,分析了几种确定基函数中心方法的流程和各自的优缺点。分析了系统聚类的基本原理及操作步骤,介绍了确定基函数中心过程中计算样本间距和类间距的多种方法,并根据聚类过程中类间距的变化情况给出了聚类停止条件,描述了其基本思想和操作方法。将用系统聚类确定基函数中心的方法应用到神经网络的构建中,介绍了改进网络训练的流程和详细步骤。在理论基础上进行改进方法的程序设计,并用实例对改进方法的有效性进行验证,最终取得的主要研究成果有:(1)研究提出了用系统聚类来确定基函数中心的新方法,并给出了这种方法的详细计算方法与步骤。将这种方法与其它方法进行对比,分析给出了这种方法的优越性。通过分析系统聚类的原理与过程,得出了新方法相比于传统方法不需要预先给出基函数中心初始点的结论,有效的避免了网络对基函数中心初始值选取敏感的问题。(2)研究给出了一种确定基函数个数的新方法。在研究系统聚类各种样本间距和类间距计算方法的基础上,提出了用类间距变化量之间的关系作为判断迭代是否停止的条件,不再需要预先给出隐含层神经元的个数,可以自组织的构建神经网络。(3)通过编程实现了算法,证明了算法的可实现性。运用MATLAB平台,设计并实现了用系统聚类确定基函数中心的方法构建神经网络。(4)利用三个实例验证了本文提出的改进方法在解决实际问题中的有效性。将用系统聚类确定基函数中心方法构建的RBF神经网络应用于函数逼近问题、分类问题、时间序列预测问题中,得到了较好的结果。将传统的基于k-means聚类方法构建的神经网络和运用系统聚类方法构建的神经网络实验结果进行比较,证明了改进方法的可行性和有效性。
[Abstract]:Radial basis function (Radial Basis Function,RBF) neural network is a kind of locally approximate three-layer feedforward neural network. Compared with other feedforward neural networks, it has the advantages of simple structure, fast convergence and not falling into the local minimum point. It has received great attention and has been widely used in many fields. In the process of constructing RBF neural network, the learning algorithm of determining the basis function center by using k-means clustering method needs to give the initial clustering center in advance. When the given initial clustering center is different, the obtained basis function center may be different. The result of network training is unstable, and the number of neurons in the hidden layer of the network needs to be given in advance, but the network structure can not be determined in advance. In order to solve this problem, a method of determining the basis function center by system clustering is proposed, which effectively solves the problem that RBF neural network is sensitive to the initial clustering center. This paper first introduces the basic principle of RBF neural network, analyzes the structure and performance of different RBF neural network, and points out the characteristics of each kind of network and the problems that need to be paid attention to. In this paper, several commonly used learning algorithms of RBF neural network are studied, and the flow chart and advantages and disadvantages of several methods for determining the center of basis function are analyzed. This paper analyzes the basic principle and operation steps of clustering, introduces several methods for calculating sample spacing and class spacing in the process of determining the center of basis function, and gives the condition of cluster stopping according to the variation of cluster spacing in clustering process. The basic ideas and methods of operation are described. The method of determining the basis function center by system clustering is applied to the construction of neural network, and the flow and detailed steps of improving network training are introduced. The program design of the improved method is carried out on the basis of the theory, and the validity of the improved method is verified by an example. The main research results are as follows: (1) A new method to determine the basis function center by system clustering is proposed in this paper. The detailed calculation method and steps of this method are given. Comparing this method with other methods, the advantages of this method are given. Based on the analysis of the principle and process of systematic clustering, the conclusion is drawn that the new method does not need to give the initial point of the center of the basis function in advance compared with the traditional method. The sensitivity of the network to the selection of the initial value of the center of the basis function is effectively avoided. (2) A new method for determining the number of basis functions is proposed. On the basis of studying various sample spacing and class spacing calculation methods of system clustering, it is proposed that the relationship between the variation of class spacing is used as the condition to judge whether the iteration is stopped or not, and the number of hidden layer neurons is no longer needed to be given in advance. The neural network can be constructed by self-organization. (3) the algorithm is realized by programming, and the realization of the algorithm is proved. Using MATLAB platform, a neural network is designed and implemented to determine the basis function center by system clustering. (4) three examples are used to verify the effectiveness of the improved method in solving practical problems. The RBF neural network based on the method of determining the basis function center by system clustering is applied to function approximation problem, classification problem and time series prediction problem, and good results are obtained. The experimental results of the traditional neural network based on k-means clustering method and the neural network based on systematic clustering method are compared, and the feasibility and effectiveness of the improved method are proved.
【学位授予单位】：东北农业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183;F224

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