Advanced Search
MyIDEAS: Login

Exact methods for variable selection in principal component analysis: Guide functions and pre-selection

Contents:

Author Info

  • Pacheco, Joaquín
  • Casado, Silvia
  • Porras, Santiago
Registered author(s):

    Abstract

    A variable selection problem is analysed for use in Principal Component Analysis (PCA). In this case, the set of original variables is divided into disjoint groups. The problem resides in the selection of variables, but with the restriction that the set of variables that is selected should contain at least one variable from each group. The objective function under consideration is the sum of the first eigenvalues of the correlation matrix of the subset of selected variables. This problem, with no known prior references, has two further difficulties, in addition to that of the variable selection problem: the evaluation of the objective function and the restriction that the subset of selected variables should also contain elements from all of the groups. Two Branch & Bound methods are proposed to obtain exact solutions that incorporate two strategies: the first one is the use of “fast” guide functions as alternatives to the objective function; the second one is the preselection of variables that help to comply with the latter restriction. From the computational tests, it is seen that both strategies are very efficient and achieve significant reductions in calculation times.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002551
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 95-111

    as in new window
    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:95-111

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: PCA; Variable selection; Branch & Bound methods; Guide functions; Filters;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Gatu, Cristian & Yanev, Petko I. & Kontoghiorghes, Erricos J., 2007. "A graph approach to generate all possible regression submodels," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 799-815, October.
    2. Michela Nardo & Michaela Saisana & Andrea Saltelli & Stefano Tarantola & Anders Hoffman & Enrico Giovannini, 2005. "Handbook on Constructing Composite Indicators: Methodology and User Guide," OECD Statistics Working Papers 2005/3, OECD Publishing.
    3. Ying Chan & Cheuk Kwan & Tan Shek, 2005. "Quality of Life in Hong Kong: the Cuhk Hong Kong Quality of Life Index," Social Indicators Research, Springer, vol. 71(1), pages 259-289, 03.
    4. Kristine Hogarty & Jeffrey Kromrey & John Ferron & Constance Hines, 2004. "Selection of variables in exploratory factor analysis: An empirical comparison of a stepwise and traditional approach," Psychometrika, Springer, vol. 69(4), pages 593-611, December.
    5. Tangian, Andranik, 2007. "Analysis of the third European survey on working conditions with composite indicators," European Journal of Operational Research, Elsevier, vol. 181(1), pages 468-499, August.
    6. Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer, vol. 73(1), pages 125-144, March.
    7. 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.
    8. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer, vol. 66(2), pages 249-270, June.
    9. Pacheco, Joaquin & Casado, Silvia & Nunez, Laura & Gomez, Olga, 2006. "Analysis of new variable selection methods for discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1463-1478, December.
    10. Brusco, Michael J. & Steinley, Douglas, 2011. "Exact and approximate algorithms for variable selection in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 123-131, January.
    11. Yutaka Kano & Akira Harada, 2000. "Stepwise variable selection in factor analysis," Psychometrika, Springer, vol. 65(1), pages 7-22, March.
    12. Hofmann, Marc & Gatu, Cristian & Kontoghiorghes, Erricos John, 2007. "Efficient algorithms for computing the best subset regression models for large-scale problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 16-29, September.
    13. Krzanowski, Wojtek J. & Hand, David J., 2009. "A simple method for screening variables before clustering microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2747-2753, May.
    14. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    15. Pacheco, Joaquín & Casado, Silvia & Núñez, Laura, 2009. "A variable selection method based on Tabu search for logistic regression models," European Journal of Operational Research, Elsevier, vol. 199(2), pages 506-511, December.
    16. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer, vol. 74(4), pages 705-726, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:95-111. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.