模型选择视域下多结点样条曲线控制点最佳数量的确定  

Determination of the Optimal Number of Control Points for Multi Node Spline Curves in the Perspective of Model Selection

作　　者：周佩佩 崔飞飞 赖嘉龙 ZHOU Pei-pei;CUI Fei-fei;LAI Jia-long(Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]江西理工大学,江西赣州341000

出　　处：《浙江工商职业技术学院学报》2023年第3期51-56,共6页Journal of Zhejiang Business Technology Institute

基　　金：2021年度江西省教育厅科学技术项目“几类动力方程解的性态研究”(编号GJJ210884)阶段性研究成果。

摘　　要：时滞微分方程的非线性和随机性增加了建模的难度,但多结点样条拟合方法可以通过选择适当的结点数目来对其进行建模。然而,结点数目的选择对拟合结果有着重要影响。通过将赤池信息量准则(AIC)、广义交叉验证(GCV)和广义赤池信息量准则(GAIC)引入到结点数目的选择问题中可以自适应地获得最佳结点数目。通过将三种准则应用到不同的三个模型中对比结果发现,相较于AIC和GCV,使用GAIC能够更有效地解决结点数目选择的问题,这种方法能够平衡拟合效果和模型复杂性,从而为时滞微分方程建模提供更可靠的结果。The nonlinearity and randomness of delay differential equations increase the difficulty of modeling,but the multi node spline fitting method can model them by selecting appropriate number of nodes.However,the selection of node numbers has a significant impact on the fitting results.By introducing the Akashi information criterion(AIC),generalized cross validation(GCV),and generalized Akashi information criterion(GAIC)into the node selection problem,the optimal number of nodes can be adaptively obtained.By applying three criteria to three different models and comparing the results,it was found that compared to AIC and GCV,using GAIC can more effectively solve the problem of node number selection.This method can balance the fitting effect and model complexity,providing more reliable results for modeling delay differential equations.

关 键 词：多结点样条 最佳结点数量 AIC GCV GAIC 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]