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Standardization of interval symbolic data based on the empirical descriptive statistics

Author

Listed:
  • Guo, Junpeng
  • Li, Wenhua
  • Li, Chenhua
  • Gao, Sa

Abstract

In many statistical analysis methods, standardization of the sample data is usually recommended to prevent the results from being strongly affected by the scale of measurement of the variables. This paper focuses on the standardization of interval data obtained by symbolic data analysis (SDA). SDA is a new data analysis technique which captures the value of a variable with a symbolic representation. The empirical descriptive statistics of the interval symbolic variable are studied first. We then proposed the standardization method of interval symbolic data and conducted a simulation study to evaluate our standardization method by using clustering analysis. An application example on e-shops of several major cities in China is given at the end of the paper. Differing from previous research, we do not require the assumption of uniformly distributed data in the interval. Our method makes the best use of the original sample information.

Suggested Citation

  • Guo, Junpeng & Li, Wenhua & Li, Chenhua & Gao, Sa, 2012. "Standardization of interval symbolic data based on the empirical descriptive statistics," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 602-610.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:602-610
    DOI: 10.1016/j.csda.2011.09.006
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    3. Francisco Carvalho & Paula Brito & Hans-Hermann Bock, 2006. "Dynamic clustering for interval data based on L 2 distance," Computational Statistics, Springer, vol. 21(2), pages 231-250, June.
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    Cited by:

    1. Wenhua Li & Junpeng Guo & Ying Chen & Minglu Wang, 2016. "A New Representation of Interval Symbolic Data and Its Application in Dynamic Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 149-165, April.

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