Ocean university of China An Improved Grey Relational Analysis Approach for Panel Data Clustering Xue-mei Li Keith.W.Hipel School of Economics, Ocean university of China

References: Li, Xuemei; Hipel, Keith W.; Dang, Yaoguo. An Improved Grey Relational Analysis Approach for Panel Data Clustering, Expert Systems With Applications,2015,42(23): 9105-9116. Ph.D Thesis

Content Abstract Research motivation Three main parts of Mean-AGRA clustering method The procedure for the Mean-AGRA clustering method Conclusions Future work

Abstract An enhanced grey clustering analysis method based on accumulation sequences using grey relational analysis (AGRA) is put forward for specifying hierarchies of clusters in panel data. Innovation point: The clustering method can handle panel data containing N samples, each of which has m time series of indicators for which the observations for a given time series can be measured at different times than other series and contain different numbers of data points compared to other series. To demonstrate how this new clustering method can be utilized in practice. It is applied to panel data consisting of 12 natural environmental indicators and 8 societal time series (m = 20) for 30 provinces (N = 30) in mainland China.

Research motivation (1) The results of calculations for some grey relational degree procedures may change if the order of the samples is altered. (2) The existing relational, evaluating and decision models for panel data are limited to time series data having equally-spaced observations at exactly the same time and over the same time period. (3) Existing relational models may not preserve certain mathematical characteristics such as what are referred to as the “index property” and the “ inner property” in the original observations of the given time series.

Research motivation (4) The critical value clustering method can be used as a kind of fast clustering method. However, sometimes faulty results may be obtained. (5) When clustering samples according to distance, incorrect clustering may occur in some circumstances.

The overall clustering approach, which is called the Mean- AGRA clustering method, contains three main parts: A sequence of transformations of each separate time series; Appropriate pairwise comparisons of the grey relational degree of an AGRA model for each pair of samples, across all samples as well as appropriate combinations thereafter, for 3 specific types of grey relational degrees; Clustering all samples according to their AGRA degrees.

Comparisons for each pair of samples Clustering calculations The original panel data Data transformations Comparisons for each pair of samples Clustering calculations Insights Obtain the accumulation sequences Simulate the accumulation sequences sequences Get the relative generation rate sequences sequences Obtain the grey relational degree of the AGRA model sequences Calculate the weight parameters Calculate grey deviation relational degree, grey difference relational degree and grey separation relational degree Cluster for all samples according to the Mean-AGRA clustering method sequences Section 2 Section 3 Section 4 See case study in Section 5

The procedure for the Mean-AGRA clustering method

Categorize ['kætəgə'raɪz] plateaux The findings clarify how, for example, the provinces in China can be meaningfully categorized according to topography into two main groups consisting of plateaux and plains.

Conclusions Therefore, the new method can handle different lengths of time series within a sample and across samples; They are useful when values occur at different times when comparing any two series; the new clustering method avoids the problem of combining two samples having a limited degree of similarity which exists in traditional method. Consequentely, the AGRA model and Mean-AGRA clustering method have expanded the scope of application of grey relational and clustering analysis.

Future work A number of works can be extended based on this research to make more reasonable and comprehensive relational and clustering analysis. Future studies could be conducted in four main directions. In terms of theory, further research on grey relational degree for panel data is needed to establish its accuracy and mathematical properties, such as consistency of different GRA models. In addition, during the simulation of original sequences, models besides the GM (1,1) model could be considered. In terms of practice, the current model and approach could be applied to challenging problems in many different fields of study which can better illustrate the advantages of AGRA model and Mean-AGRA clustering method. In addition, the effectiveness and adaptation of AGRA model and Mean- AGRA clustering method in expert and intelligent systems will be our focus of future research. Consequently, these studies are in progress.

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