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Principal component analysis for histogram-valued data

Author

Listed:
  • J. Le-Rademacher

    (Mayo Clinic)

  • L. Billard

    (University of Georgia)

Abstract

This paper introduces a principal component methodology for analysing histogram-valued data under the symbolic data domain. Currently, no comparable method exists for this type of data. The proposed method uses a symbolic covariance matrix to determine the principal component space. The resulting observations on principal component space are presented as polytopes for visualization. Numerical representation of the resulting polytopes via histogram-valued output is also presented. The necessary algorithms are included. The technique is illustrated on a weather data set.

Suggested Citation

  • J. Le-Rademacher & L. Billard, 2017. "Principal component analysis for histogram-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 327-351, June.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:2:d:10.1007_s11634-016-0255-9
    DOI: 10.1007/s11634-016-0255-9
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    References listed on IDEAS

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    1. 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.
    2. J. Le-Rademacher & L. Billard, 2013. "Principal component histograms from interval-valued observations," Computational Statistics, Springer, vol. 28(5), pages 2117-2138, October.
    3. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    4. Sun Makosso-Kallyth & Edwin Diday, 2012. "Adaptation of interval PCA to symbolic histogram variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(2), pages 147-159, July.
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    Cited by:

    1. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Liu, Jicheng & Lin, Xiangmin, 2019. "Empirical analysis and strategy suggestions on the value-added capacity of photovoltaic industry value chain in China," Energy, Elsevier, vol. 180(C), pages 356-366.

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