【摘要】：徑向基函數(shù)(Radial Basis Function,RBF)神經(jīng)網(wǎng)絡(luò)是一種局部逼近的三層前饋型神經(jīng)網(wǎng)絡(luò),相比于其它前饋型神經(jīng)網(wǎng)絡(luò)有結(jié)構(gòu)簡(jiǎn)單、收斂速度快、不會(huì)陷入局部最小值點(diǎn)等優(yōu)點(diǎn),受到了極大關(guān)注并在許多領(lǐng)域得到了廣泛應(yīng)用。在RBF神經(jīng)網(wǎng)絡(luò)的構(gòu)建過程中,運(yùn)用k-means聚類方法確定基函數(shù)中心的學(xué)習(xí)算法需要預(yù)先給出初始聚類中心,當(dāng)給定的初始聚類中心不同時(shí),得到的基函數(shù)中心可能是不同的,導(dǎo)致網(wǎng)絡(luò)訓(xùn)練結(jié)果不穩(wěn)定,并且網(wǎng)絡(luò)隱含層神經(jīng)元的個(gè)數(shù)需要提前給出,但往往網(wǎng)絡(luò)結(jié)構(gòu)是不能預(yù)先確定的。針對(duì)這一問題,提出了運(yùn)用系統(tǒng)聚類確定基函數(shù)中心的方法,從而有效的解決了RBF神經(jīng)網(wǎng)絡(luò)對(duì)初始聚類中心敏感的問題。本文首先介紹了RBF神經(jīng)網(wǎng)絡(luò)的基本原理,對(duì)不同RBF神經(jīng)網(wǎng)絡(luò)的結(jié)構(gòu)和性能進(jìn)行了分析,指出各種網(wǎng)絡(luò)的特點(diǎn)和需要注意的問題。研究了RBF神經(jīng)網(wǎng)絡(luò)幾種常用的學(xué)習(xí)算法,分析了幾種確定基函數(shù)中心方法的流程和各自的優(yōu)缺點(diǎn)。分析了系統(tǒng)聚類的基本原理及操作步驟,介紹了確定基函數(shù)中心過程中計(jì)算樣本間距和類間距的多種方法,并根據(jù)聚類過程中類間距的變化情況給出了聚類停止條件,描述了其基本思想和操作方法。將用系統(tǒng)聚類確定基函數(shù)中心的方法應(yīng)用到神經(jīng)網(wǎng)絡(luò)的構(gòu)建中,介紹了改進(jìn)網(wǎng)絡(luò)訓(xùn)練的流程和詳細(xì)步驟。在理論基礎(chǔ)上進(jìn)行改進(jìn)方法的程序設(shè)計(jì),并用實(shí)例對(duì)改進(jìn)方法的有效性進(jìn)行驗(yàn)證,最終取得的主要研究成果有:(1)研究提出了用系統(tǒng)聚類來(lái)確定基函數(shù)中心的新方法,并給出了這種方法的詳細(xì)計(jì)算方法與步驟。將這種方法與其它方法進(jìn)行對(duì)比,分析給出了這種方法的優(yōu)越性。通過分析系統(tǒng)聚類的原理與過程,得出了新方法相比于傳統(tǒng)方法不需要預(yù)先給出基函數(shù)中心初始點(diǎn)的結(jié)論,有效的避免了網(wǎng)絡(luò)對(duì)基函數(shù)中心初始值選取敏感的問題。(2)研究給出了一種確定基函數(shù)個(gè)數(shù)的新方法。在研究系統(tǒng)聚類各種樣本間距和類間距計(jì)算方法的基礎(chǔ)上,提出了用類間距變化量之間的關(guān)系作為判斷迭代是否停止的條件,不再需要預(yù)先給出隱含層神經(jīng)元的個(gè)數(shù),可以自組織的構(gòu)建神經(jīng)網(wǎng)絡(luò)。(3)通過編程實(shí)現(xiàn)了算法,證明了算法的可實(shí)現(xiàn)性。運(yùn)用MATLAB平臺(tái),設(shè)計(jì)并實(shí)現(xiàn)了用系統(tǒng)聚類確定基函數(shù)中心的方法構(gòu)建神經(jīng)網(wǎng)絡(luò)。(4)利用三個(gè)實(shí)例驗(yàn)證了本文提出的改進(jìn)方法在解決實(shí)際問題中的有效性。將用系統(tǒng)聚類確定基函數(shù)中心方法構(gòu)建的RBF神經(jīng)網(wǎng)絡(luò)應(yīng)用于函數(shù)逼近問題、分類問題、時(shí)間序列預(yù)測(cè)問題中,得到了較好的結(jié)果。將傳統(tǒng)的基于k-means聚類方法構(gòu)建的神經(jīng)網(wǎng)絡(luò)和運(yùn)用系統(tǒng)聚類方法構(gòu)建的神經(jīng)網(wǎng)絡(luò)實(shí)驗(yàn)結(jié)果進(jìn)行比較,證明了改進(jìn)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.
【學(xué)位授予單位】：東北農(nóng)業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP183;F224

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