灰色Verhulst型LS-SVM的构建及参数估计方法  

Construction of Grey Verhulst LS-SVM and Method of Parameter Estimation

作　　者：周德强[1] Zhou Deqiang(School of Information and Mathematics,Yangtze University,Jingzhou Hubei 434023,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《统计与决策》2020年第12期59-63,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(61503047);湖北省自然科学基金资助项目(2013CFA053);湖北省科技厅技术创新专项(2018ADC068);长江大学数学与应用数学研究所开放基金(KF1506)。

摘　　要：为提高灰色Verhulst模型的预测能力,文章用统计学习理论的观点研究灰色Verhulst模型的建立问题。通过两种方式构造了以背景值序列和原始序列为训练样本的灰色Verhulst型LS-SVM,将一维样本空间里的Verhulst模型转化为一个二维特征空间里的LS-SVM模型,进而将Verhulst模型的灰参数的估计问题转化为一个LS-SVM模型的回归系数估计问题,实现了小样本体系下灰色Verhulst模型的建立和参数估计。实验结果表明该方法是可行且有效的,可有效提高Verhulst模型的推广性,比传统参数估计方法的预测精度更高。In order to improve the forecasting accuracy of the grey Verhulst model,this paper studies the establishment of grey Verhulst model from the viewpoint of statistical learning theory. The paper first uses two ways to construct the background values and the original sequences as the training sample of grey Verhulst model LS-SVM, and then transforms the Verhulst model in one-dimensional sample space into an LS-SVM model in two dimensional feature space. Finally, the paper transforms the estimation of Verhulst grey parameters into a regression coefficient estimation of LS-SVM model, realizing the establishment of grey Verhulst model and parameter estimation in the small sample system. The experimental results show that the proposed method is feasible and effective, which can effectively improve the extension of Verhulst model, and that the prediction accuracy is higher than that of the traditional parameter estimation method.

关 键 词：结构风险最小化 参数估计 最小二乘支持向量机 灰色VERHULST模型 灰色Verhulst型LS-SVM 

分 类 号：O212[理学—概率论与数理统计]