分片合并模型树光滑逼近算法  

Smooth approximation algorithm based on split-merge model trees

作　　者：冯云方[1] 王书宁[1] 王伟[1] 

机构地区：[1]清华大学自动化系,北京100084

出　　处：《清华大学学报（自然科学版）》2003年第7期869-872,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(69974023;69934010);清华大学信息学院创新基金资助项目

摘　　要：针对已知样本数据建立非线性函数模型的问题,提出了分片合并模型树光滑逼近算法。在区域线性模型树算法的基础上,采用区域分片和区域合并两个算法将输入空间划分为若干子区域,对每个子区域使用线性函数进行逼近,并构建该子区域上的加权函数,生成基函数展开方式的全局表达,从而获得光滑的任意精度逼近结果。分片合并算法使得相同的线性函数可以在非凸甚至非连通的区域上起作用。在参数数量相同的情况下,其逼近精度比区域线性模型树算法有显著提高。仿真结果表明:该算法是解决这类建模问题的有效方法。A smooth approximation alg or ithm based on split-merge model trees was developed for sample data-based mode ling of nonlinear functions. The local linear model trees algorithm was used to partitions the input space into several areas using the split-merge algorithm. A piece-wise linear function was used to approximate and construct weighting f unctions in each region. The full expression of the basis functions was then use d to obtain smooth approximations with arbitrary precision. The split-merge alg orithm simultaneously applies some of the linear functions on several non-conve x or non-connected regions. A comparison using the same number of parameters as in the local linear model trees algorithm shows that this smooth approximation algorithm enhances the approximation precision. 

关 键 词：分片线性逼近 分片合并模型树光滑逼近算法 线性函数 加权函数 区域线性模型树算法 非线性系统 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O231.2[自动化与计算机技术—计算机科学与技术]