分维权重样条插值预测算法及应用  

Prediction Algorithm for Fractal-dimension Weight of Spline Interpolation and Its application

作　　者：杨利华[1] 詹棠森[1] 吴倩[1] 付长春[1] 周美旭[1] 程羽[1] 

机构地区：[1]景德镇陶瓷学院信息工程学院,江西景德镇333403

出　　处：《数学的实践与认识》2014年第24期207-212,共6页Mathematics in Practice and Theory

基　　金：2013教育部人文社科基金项目(13YJA760064);国家自然科学基金(61262038;61202313);江西省自然科学基金(20122BAB201016;20122BAB211033);2013景德镇市科研项目

摘　　要：基于高维数据预测方法的应用,提出一种分维权重样条插值预测算法.通过高维数据的各维,建立样本各维数据与对应权重的网络结构关系,网络的结点个数与样本的个数无关.通过训练样本各维权重所满足的线性方程组得到各维的权值,再根据样本的各维数据值和所得到的对应权值进行三次样条插值,得到各维数据值的权值函数,而不是传统方法的常数,这克服了个别数据变化所带来的整体度量值发生较大变化的缺点.数值仿真实验表明:分维权重样条插值预测算法不失是一种稳定而灵活的算法,而且预测的精度较高,可以根据样条插值函数得到样本各维的权值.A prediction algorithm for fractal-dimension weight and spline interpolation based on application of high-dimensional data prediction is proposed.Network structure relations between dimensional data of the samples and the corresponding weight is established,the number of network nodes are not related to the number of samples.The weight of each dimension is obtained by linear equations that are satisfied with fractal-dimension weight of trained samples,and fractal-dimension weight function is got,on the basis of cubic spline interpolation between each dimension data and corresponding weight,it is not constants which are got by the popular learning algorithm.This overcomes the disadvantage of large changes caused by changes of the individual data.Some simulation examples are presented to show that the algorithm is better and flexible,and has good precision,the every dimension weight of each data is got through spline interpolation function.

关 键 词：分维 样条插值 权重函数 预测 

分 类 号：O241.3[理学—计算数学]