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Discarding Variables in a Principal Component Analysis: Algorithms for All-Subsets Comparisons

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  • António Pedro Duarte Silva

    (Universidade Católica Portuguesa at Porto)

Abstract

Summary The traditional approach to the interpretation of the results from a Principal Component Analysis implicitly discards variables that are weakly correlated with the most important and/or most interesting Principal Components. Some authors argue that this practice is potentially misleading and that it is preferable to take a variable selection approach, comparing variable subsets according to appropriate approximation criteria. In this paper, we propose algorithms for the comparison of all possible subsets according to some of the most important comparison criteria proposed to date. The computational effort of the proposed algorithms is studied and it is shown that, given current computer technology, they are feasible for problems involving up to thirty variables. A free-domain software implementation can be downloaded from the Internet.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:2:d:10.1007_s001800200105
    DOI: 10.1007/s001800200105
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    References listed on IDEAS

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    1. 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.
    2. I. T. Jolliffe, 1973. "Discarding Variables in a Principal Component Analysis. Ii: Real Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(1), pages 21-31, March.
    3. P. Robert & Y. Escoufier, 1976. "A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 257-265, November.
    4. Duarte Silva, António Pedro, 2001. "Efficient Variable Screening for Multivariate Analysis," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 35-62, January.
    5. I. T. Jolliffe, 1972. "Discarding Variables in a Principal Component Analysis. I: Artificial Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 160-173, June.
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    Cited by:

    1. A. Pedro Duarte Silva, 2009. "Exact and heuristic algorithms for variable selection: Extended Leaps and Bounds," Working Papers de Economia (Economics Working Papers) 01, Católica Porto Business School, Universidade Católica Portuguesa.
    2. 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.
    3. 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.
    4. Brosnan, Kylie & Grün, Bettina & Dolnicar, Sara, 2018. "Identifying superfluous survey items," Journal of Retailing and Consumer Services, Elsevier, vol. 43(C), pages 39-45.
    5. 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.
    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.
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