基于灰色可能度函数的面板数据聚类方法

Clustering method based on the grey possibility degree function for panel data

针对静态灰色可能度函数聚类方法的局限性,综合考虑评价指标发展趋势、指标权重和时间权重的影响,构建一种体现发展趋势的灰色可能度函数聚类模型用于解决面板数据问题.该方法引入发展因子概念,用于表示观测值的发展趋势;对于观测对象在不同时刻的观测值,运用发展因子将观测值集结为发展作用值,并利用时间权重对包含发展作用值的面板数据进行降维,从而获得信息集结值.运用所提出的权重求解法确定每个指标各时刻指标权重,再根据离差平方和最小化方法优化求解总时段综合指标权重,并对降维后的信息集结值进行灰色可能度函数聚类分析.最后,通过对中国10个城市5年宏观经济状况的聚类分析,验证所提出模型的有效性和可行性,实现了灰色可能度函数聚类方法的面板数据处理.

Aiming at the limitations of the static grey clustering method, a grey possibility clustering method is proposed to solve the problems of panel data, synthetically considering the growing trend, index weight, and time weight. In this method, the development factor is defined to express development tendency for observed values. Subsequently, according to the time weight in different time point, each index value of the evaluation object is aggregated into development action value by growing factor, and development action values are aggregated to obtain information assemble values for reducing the dimension of the panel data. Meanwhile, the index weights in different time points are determined by using the proposed method. Apart from these above index weights, the comprehensive weight for the whole time period is measured by minimizing the sum of squares of deviations. Furthermore, the information assemble values after information aggregation are clustering analyzed by utilizing the grey possibility function. Finally, the experimental results generated by using the economic and social data from China’s 10 cities in 5 years verify the practicality and effectiveness of this proposed model, and the proposed model realizes the grey possibility function clustering for panel data.