“降维”技术在多变量综合评价中的应用——基于TOPSIS和GRA的实证检验  

Application of " Dimensionality Reduction" Technique in Multivariate Analysis Evaluation:An Empirical Test Based on TOPSIS and GRA

作　　者：李兴国[1] 张莉莉[2] LI Xing-guo ZHANG Li-li(Higher Education Development Research Center of Yanshan Universiey The Superrision of the Quditing Office of Yanshan University,Qinhuangdao 066004, Hebei)

机构地区：[1]燕山大学高等教育发展研究中心,河北秦皇岛066004 [2]燕山大学监察审计处,河北秦皇岛066004

出　　处：《徐州工程学院学报（社会科学版）》2016年第6期47-51,共5页Journal of Xuzhou Institute of Technology：Social Sciences Edition

基　　金：2015年河北省文化艺术科学规划项目"河北省文化产业竞争力提升动力机理与实现路径研究"(HBWY2015-Y-F007)

摘　　要："降维"是多元统计分析中对具有相关性和重叠性信息原始变量进行简化的一种方法,降维后的抽象变量能够保留众多原始变量的主要信息。通过将降维的思想扩展到多变量综合评价技术,选取2012年河北省各城市代表性经济指标数据,对降维前后的TOPSIS和GRA方法排序结果进行实证检验。结果表明:降维后的TOPSIS法与降维前的排序结果在0.01水平上显著相关,且相关系数高达0.9以上;降维后的GRA法与降维前的排序结果完全一致。表明降维方法在多变量综合评价与决策中具有良好的应用前景。＂ Dimension reduction＂ is a method in multivariate statistical analysis to simplify the original variable of correlation and overlaps information.Abstract variables getting in dimension reduction can retain the main information of original variables.In this paper,we expand the idea of dimension reduction to multi-objective comprehensive evaluation technology,selection of typical economic index data from city in Hebei Province in 2012,carried on the empirical test before and after the dimension reduction of TOPSIS and the GRA method sorting result.The results showed that the reduction of TOPSIS method and dimension reduction before sorting result in significant correlation at the 0.01 level,and the correlation coefficient is as high as 0.9.The reduced GRA method is completely consistent with the prior sorting result which proves that the dimensionality reduction method has a good application prospect in multivariable comprehensive evaluation and decision.

关 键 词：降维 多变量评价 因子分析 TOPSIS GRA 

分 类 号：F207[经济管理—国民经济]