文档介绍：基于多层径向基函数网络的实函数逼近过程的研究
摘要
经济学家和金融学家在研究经济金融现象时,常常选用简单易行的线性模型和稍微复杂的非线性模型。这类模型往往要求得到具体的函数表达式,表达式中的各个因素也是明确的,然而经济金融现象的复杂性往往使学者们无法考虑到所有的影响因素,即使考虑到当年的影响因素,也很难准确的把握以后年度里产生的新的影响因素,以至于经济金融模型的预测精确度不高。径向基函数网络具有逼近任意非线性函数的能力,能建立起更高精确的数学模型,更好地预测未来的变化趋势。多层径向基函数网络是在单层径向基函数网络的基础上提出来的。本文首先介绍了多层径向基函数网络的基本原理,然后通过计算机模拟实验研究网络的结构和参数对是函数逼近精度的影响,同时还比较了单层径向基函数网络和多层径向基函数网络对实函数逼近能力的大小。实验表明,与单层径向基函数网络相比多层径向基函数网络有很高的实函数逼近能力,并且逼近精度与网络结构的关系是具有可塑性的,即网络能通过调整自己的结构来实现最佳逼近精度。
关键词:径向基函数;径向基函数网络;多层径向基函数网络;k-均值算法
Abstract
When Economists and financiers study the economic Phenomenon, they often use a simple linear model and a plicated nonlinear model. Such models often require a specific function expression, and each factor also should be clear. To be disappointed , the economic Phenomenon is often plicated that all factors can’t be taken into account, even economists have considered this year, it is also difficult to accurately grasp the subsequent years in the emergence of new factors, and the economic and financial model prediction is not expected. work has a strong ability to approximate any nonlinear function, and establish a more precise mathematical model to predict better future trend. Multi-layer work build on Single layer work. In this context, we will introduce the principle of Multi-layer work and then use puter experiment to simulate work structure and parameters of the function approximation accuracy, at the same time, we pare the ability of Single layer work with Multi-layer work to approximate real functions. Experiment shows that Multi-layer work is better to approximate real functions, the relationship of approximation accuracy work structure is malleable, that is to say, network can regulate its structure to achieve the best approximation accuracy.
Keywords: RBF ;work ;Multi-layer work ;k-means
目录
第一章引言 1
(一) 研究的背景 1
(二) 研究的目的与现实的意义 1
第二章综述 1
(一) 径向基函数在经济金融领域的运用 1
(二) 混沌序列理论 3
第三章径向基函数网络 4
(一) 径向基函数的基本概念 4
(二) 径向基函数网络 5
(三) 径向基函数网络的几种典型的学****方法 6
第四章多层径向基函数网络 8
(一) 多层