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A two-stage principal component analysis of symbolic data using equicorrelated and jointly equicorrelated covariance structures

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  • Anuradha Roy

    (UTSA)

Abstract

A new approach to derive the principal components of symbolic data is proposed in this article. This is done in two stages: first getting eigenblocks and eigenmatrices of the variance-covariance matrix, and then analyzing these eigenblocks and the corresponding principal vec- tors together in some seemly sense to get the adjusted eigenvalues and the corresponding eigenvectors of the interval data. The proposed method is very efficient in two-level and three-level symbolic data sets. Results illustrating the accuracy and appropriateness of the new method over the existing methods are presented. We have clearly shown with the help of examples that our proposed method for principal component analysis (PCA) of three-level symbolic data generalizes the commonly used PCA for multivariate data.

Suggested Citation

  • Anuradha Roy, 2014. "A two-stage principal component analysis of symbolic data using equicorrelated and jointly equicorrelated covariance structures," Working Papers 0164mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0164mss
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    File URL: http://interim.business.utsa.edu/wps/mss/0006MSS-253-2014.pdf
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    References listed on IDEAS

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    1. Giordani, Paolo & Kiers, Henk A.L., 2006. "A comparison of three methods for principal component analysis of fuzzy interval data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 379-397, November.
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    Cited by:

    1. Arkadiusz Koziol & Anuradha Roy & Roman Zmyslony & Ricardo Leiva & Miguel Fonseca, 2016. "Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure," Working Papers 0149mss, College of Business, University of Texas at San Antonio.
    2. Ricardo Leiva & Anuradha Roy, 2016. "Multi-level multivariate normal distribution with self-similar compound symmetry covariance matrix," Working Papers 0146mss, College of Business, University of Texas at San Antonio.
    3. Hao, Chengcheng & Liang, Yuli & Roy, Anuradha, 2015. "Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 113-120.

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    More about this item

    Keywords

    Jointly equicorrelated covariance structure; symbolic data; Two-stage principal com- ponent analysis;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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