灰色关联聚类降维新方法及其应用  

A New Dimension Reduction Method of Grey Correlation Clustering and Its Application

作　　者：毛翠微 何承香 曾波 MAO Cuiwei;HE Chengxiang;ZENG Bo(Chongqing Key Laboratory of Spatial Data Mining and Big Data Integration for Ecology and Environment,Chongqing Finance and Economics College,Chongqing 401320,China;School of Logistics Engineering,Chongqing Finance and Economics College,Chongqing 401320,China;School of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆财经学院生态环境空间数据挖掘与大数据集成重庆市重点实验室,重庆401320 [2]重庆财经学院物流工程学院,重庆401320 [3]重庆工商大学管理科学与工程学院,重庆400067

出　　处：《复旦学报（自然科学版）》2023年第6期703-713,共11页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(72071023);重庆市教育委员会科学技术研究重大项目(KJZD-M202300801);重庆市教育委员会科学技术研究重点项目(KJZD-K202202102);重庆市自然科学基金(CSTB2023NSCQ-MSX0365,CSTB2023NSCQ-MSX0380);重庆市研究生导师团队建设项目(yds223006)。

摘　　要：灰色关联聚类是小数据条件下对系统的多指标问题进行降维处理的一种常用方法。然而,当前灰色关联聚类方法仅考虑了主变量与待聚变量之间的关联度,而忽略了待聚变量两两之间的关联性,导致同组聚类变量某些指标之间存在弱关联。为此,本文以灰色面积关联度模型为基础,提出了一种变量筛选与聚类降维的新方法,并以江苏省人口密度影响因素的筛选与聚类为例,介绍和分析了自变量的初筛与聚类分组、组内自变量的筛选与唯一性分组及自变量的最终确定等过程。新方法确保了聚类组内变量两两之间的强关联性这一基本原则,对完善灰色聚类模型具有积极意义。Grey relational clustering is a common method to reduce the dimension of multi index problems under the condition of small data.However,the current grey relational clustering method only considers the correlation degree between the main variable and the variables to be clustered,and ignores the correlation between the two variables to be clustered,resulting in weak correlation between some indexes of the same group of clustering variables.Therefore,based on the grey area correlation model,this paper puts forward a new method of variable screening and clustering dimensionality reduction.Taking the screening and clustering of influencing factors of population density in Jiangsu Province as an example,this paper introduces and analyzes the processes of initial screening and clustering grouping of independent variables,screening and uniqueness grouping of independent variables in the group,and final determination of independent variables.The new method ensures the basic principle of strong correlation between two variables in the clustering group,which is of positive significance to improve the grey clustering model.

关 键 词：灰色关联聚类 灰色面积关联度 变量筛选 聚类降维 

分 类 号：C934[经济管理—管理学] O159[理学—数学]