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Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components

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  • W. J. Krzanowski

Abstract

A common objective in exploratory multivariate analysis is to identify a subset of the variables which conveys the main features of the whole sample. Analysis of a well‐known multivariate data set shows that methods currently available for selecting variables in principal component analysis may not lead to an appropriate subset. A new selection method, based on Procrustes Analysis, is proposed and shown to lead to a better subset for the data first analysed. Some supporting Monte Carlo results are presented, and implications for other multivariate techniques are briefly discussed.

Suggested Citation

  • W. J. Krzanowski, 1987. "Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(1), pages 22-33, March.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:1:p:22-33
    DOI: 10.2307/2347842
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    Cited by:

    1. Giancarlo Diana & Chiara Tommasi, 2002. "Cross-validation methods in principal component analysis: A comparison," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(1), pages 71-82, February.
    2. Drgoňa, Ján & Picard, Damien & Kvasnica, Michal & Helsen, Lieve, 2018. "Approximate model predictive building control via machine learning," Applied Energy, Elsevier, vol. 218(C), pages 199-216.
    3. Tangian, Andranik S., 2017. "Selection of questions for VAAs and the VAA-based elections," Working Paper Series in Economics 100, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    4. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    5. Cadima, Jorge & Cerdeira, J. Orestes & Minhoto, Manuel, 2004. "Computational aspects of algorithms for variable selection in the context of principal components," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 225-236, September.
    6. Pacheco, Joaquín & Casado, Silvia & Porras, Santiago, 2013. "Exact methods for variable selection in principal component analysis: Guide functions and pre-selection," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 95-111.
    7. Cumming, J.A. & Wooff, D.A., 2007. "Dimension reduction via principal variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 550-565, September.
    8. Michael Greenacre, 2024. "The chiPower transformation: a valid alternative to logratio transformations in compositional data analysis," 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. 18(3), pages 769-796, September.
    9. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Michael Greenacre, 2023. "The chi-square standardization, combined with Box-Cox transformation, is a valid alternative to transforming to logratios in compositional data analysis," Economics Working Papers 1857, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Brusco, Michael J., 2014. "A comparison of simulated annealing algorithms for variable selection in principal component analysis and discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 38-53.
    12. Jolanta Batog & Jakub Frankowski & Aleksandra Wawro & Agnieszka Łacka, 2020. "Bioethanol Production from Biomass of Selected Sorghum Varieties Cultivated as Main and Second Crop," Energies, MDPI, vol. 13(23), pages 1-12, November.
    13. António Pedro Duarte Silva, 2002. "Discarding Variables in a Principal Component Analysis: Algorithms for All-Subsets Comparisons," Computational Statistics, Springer, vol. 17(2), pages 251-271, July.
    14. Özge Kuran & M. Revan Özkale, 2024. "The ridge prediction error sum of squares statistic in linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 757-773, October.
    15. Jérome SARACCO & Marie CHAVENT & Vanessa KUENTZ, 2010. "Clustering of categorical variables around latent variables," Cahiers du GREThA (2007-2019) 2010-02, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).

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