Research On Clustering Method Of Grey Panel Data And Its Applications

With the continuous progress of social economy,people are facing more complex problems,and the available information is more and more uncertain,showing the characteristics of "small sample,poor information".Some panel data also exhibit this characteristic,which we call gray panel data.Most clustering methods require a large amount of data,which is easy to fail when the amount of data is small,and gray clustering can just solve the failure problem of clustering with small samples.But now relevant research results mainly focus on the panel clustering in the form of point value.As far as the author knows,there has been no in-depth and complete exploration on how to cluster the grey panel data.This paper studies the common gray clustering methods(gray association clustering,gray whitening weight function clustering),and proposes two gray clustering methods based on gray panel data,and the whitening weight function clustering method of gray panel data is applied to the air quality evaluation of eight major cities including Hangzhou.The specific research content is developed from the following aspects.(1)Introduced the concept of gray panel data,and constructed a gray relational clustering method based on the form of gray panel data.It specifically includes: realizing conversion of interval gray numbers to construct a gray correlation degree based on interval gray numbers,and introducing the idea of generalized grey relation,will be calculated under different time integration of the grey correlation matrix,and according to the clustering of the critical value,finally,a numerical example,proves the effectiveness and feasibility.(2)A clustering method of whitening weight function based on gray panel data is proposed.Firstly,the application range of whitening weight function is expanded,and a whitening weight function based on interval gray number is derived.Afterwards,aiming at the problem that the existing model cannot be applied to gray panel data,the scope of its application is expanded,and an extended method for determining the clustering weight of gray panel data is proposed.According to the principle of new information priority,the grey clustering coefficient matrix at different moments is integrated to obtain the comprehensive grey clustering coefficient matrix.Finally,an example is used to prove the effectiveness and feasibility of the method.(3)Apply the whitening weight function clustering method based on gray panel data to the air quality evaluation of eight major cities including Hangzhou and corresponding suggestions were given based on the evaluation results,which proved the scientificity,feasibility and Effectiveness.