Exact methods for variable selection in principal component analysis: Guide functions and pre-selection
AbstractA 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 57 (2013)
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/locate/csda
PCA; Variable selection; Branch & Bound methods; Guide functions; Filters;
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- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer, vol. 66(2), pages 249-270, June.
- 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.
- Yutaka Kano & Akira Harada, 2000. "Stepwise variable selection in factor analysis," Psychometrika, Springer, vol. 65(1), pages 7-22, March.
- 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.
- 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.
- 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.
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