Computational aspects of algorithms for variable selection in the context of principal components

Computational Statistics and Data Analysis

Volumn 47, Issue 2 SPEC. ISS., 2004, Pages 225-236

  Cadima, Jorge ^a   Cerdeira, J Orestes ^a   Minhoto, Manuel ^b  

^a INSTITUTO SUPERIOR DE AGRONOMIA   (Portugal)

^b UNIVERSITY OF ÉVORA   (Portugal)

Author keywords

Combinatorial optimization; Heuristics; Principal components; Principal variables; Variable selection

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; PRINCIPAL COMPONENT ANALYSIS; PROBLEM SOLVING; SET THEORY;

COMBINATORIAL OPTIMIZATION; PRINCIPLE VARIABLES; VARIABLE SELECTION;

COMPUTATIONAL METHODS;

EID: 4444375377     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2003.11.001     Document Type: Article

References (26)

1. Aarts E.H.L., Korst J.H.M., van Laarhoven P.J.M. Simulated annealing. Aarts E., Lenstra J.K. Local Search in Combinatorial Optimization. 1997;91-120 Wiley, New York.
2. Becker, R., Chambers, J., Wilks, A., 1988. The New S Language. A programming Environment for Data Analysis and Graphics. Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, CA.
3. Bonifas I., Escoufier Y., Gonzalez P.L., Sabatier R. Choix de variables en analyse en composants principales. Rev. Statist. Appl. 23:1984;5-15.
4. Cadima J., Jolliffe I.T. Loadings and correlations in the interpretation of principal components. J. Appl. Statist. 22(2):1995;203-214.
5. Cadima J., Jolliffe I.T. Variable selection and the interpretation of principal subspaces. J. Agricultural, Biol. Environ. Statist. 6(1):2001;62-79.
6. Draper N., Smith H. Applied Regression Analysis. 3rd Edition:1998;Wiley, New York.
7. Duarte Silva A.P. Efficient variable screening for multivariate analysis. J. Multivariate Anal. 76:2001;35-62.
8. Duarte Silva A.P. Discarding variables in principal component analysis algorithms for all-subset comparisons. Comput. Statist. 17:2002;251-271.
9. de Falguerolles A., Jmel S. Un critère de choix de variables en analyse en composants principales fondé sur des modèles graphiques gaussiens particuliers. Canad. J. Statist. 21(3):1993;239-256.
10. Fedorov, V., Gruben, D., Leonov, S., 1999. Direct method of selecting informative variables. Smith Kline Beecham Biostatistics and Data Sciences Technical Report 1999-02.
11. Furnival G.M., Wilson R.W. Regressions by leaps and bounds. Technometrics. 16:1974;499-511. (reprinted in Technometrics 42, 1, 69-79).
12. Furnival G.M., Wilson R.W. Regressions by leaps and bounds. Technometrics. 16:1974;499-511. (reprinted in Technometrics 42, 1, 69-79).
13. Golub G., Van Loan C. Matrix Computations. 1996;Johns Hopkins University Press, Baltimore, MD.
14. Gonzalez P.L., Evry R., Cléroux R., Rioux B. Selecting the best subset of variables in principal component analysis. Momirovic K., Mildner V. 1990;115-120 Physica-Verlag, Compstat.
15. Jolliffe I.T. Discarding variables in a principal component analysis, I. Artificial data Appl. Statist. 21:1972;160-173.
16. Jolliffe I.T. Discarding variables in a principal component analysis, II. Real data Appl. Statist. 22:1973;21-31.
17. Jolliffe I.T. Principal Component Analysis. 2nd Edition:2002;Springer, New York.
18. Krzanowski W.J. Selection of variables to preserve multivariate data structure using principal components. Appl. Statist. 36:1987;22-33.
19. McCabe G.P. Principal variables. Technometrics. 26(2):1984;137-144.
20. McCabe, G.P., 1986. Prediction of principal components by variables subsets. Technical Report 86-19, Department of Statistics, Purdue University.
21. Mühlenbein H. Genetic algorithms. Aarts E., Lenstra J.K. Local Search in Combinatorial Optimization. 1997;137-171 Wiley, New York.
22. Ramsay J.O., ten Berge J., Styan G.P.H. Matrix correlation. Psychometrika. 49(3):1984;403-423.
23. Robert P., Escoufier Y. A unifying tool for linear multivariate statistical methods. the RV-coefficient Appl. Statist. 25(3):1976;257-265.
24. Tanaka Y., Mori Y. Principal Component Analysis based on a subset of variables. variable selection and sensitivity analysis American J. Math. Management Sci. 17(1 & 2):1997;61-89.
25. Tovey C.A. Local improvement on discrete structures. Aarts E., Lenstra J.K. Local Search in Combinatorial Optimization. 1997;57-89 Wiley, New York.
26. Whittaker J. Graphical Models in Applied Multivariate Statistics. 1990;Wiley, New York.