Dimensionality choice in principal components analysis via cross-validatory methods

Chemometrics and Intelligent Laboratory Systems

Volumn 130, Issue , 2014, Pages 6-13

  Eshghi, Peyman ^a  

^a GLAXOSMITHKLINE   (United Kingdom)

Author keywords

Cross validation; NIPALS; PCA

Indexed keywords

ALGORITHM; ARTICLE; INTERMETHOD COMPARISON; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; RELIABILITY; SIMULATION; VALIDATION PROCESS;

EID: 84884972897     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2013.09.004     Document Type: Article

References (20)

1. Jackson J.Edward A User's Guide to Principal Components 2003, John Wiley & Sons.
2. Wold S. Cross-validatory estimation of the number of components in factor and principal components models. Technometrics 1978, 20:397-405.
3. Eastment H.T., Krzanowski W.J. Cross-validatory choice of the number of components from a principal component analysis. Technometrics 1982, 24:73-77.
4. Wold H. Estimation of principal components and related models by iterative least squares. Multivariate Analysis 1966, 391-420. Academic Press, NY. P.R. Krishnaiah (Ed.).
5. Shao J. Linear model selection by cross-validation. J. Am. Stat. Assoc. 1993, 88:486-494.
6. The UMETRICS website, SIMCA-P+11 http://www.umetrics.com/.
7. Bro R., Kjeldahl K., Smilde A.K., Kiers H.A.L. Cross-validation of component models: a critical look at current methods. Anal. Bioanal. Chem. 2008, 390:1241-1251.
8. The R Project for Statistical Computing, R version 2.8.1 http://www.r-project.org/.
9. Hotelling H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 1933, 24:417-441.
10. Jolliffe I.T. Principal Component Analysis, Series: Springer Series in Statistics 2002, Springer, NY. 2nd edn.
11. Mardia k, Kent J., Bibby J. Multivariate Analysis 1979, Academic Press, London.
12. Nelson Philip R.C., Taylor Paul A., MacGregor John F. Missing data methods in PCA and PLS: score calculations with incomplete observations. Chemom. Intell. Lab. Syst. 1996, 35(1):45-65.
13. Rubin D.B. Inference and missing data. Biometrika 1976, 63:581-592.
14. Velicer W.F. Determining the number of components from the matrix of partial correlations. Psychometrika 1976, 41:321-327.
15. Cattell R.B., Jaspers J. A general plasmode for factor analytic exercises and research. Multivar. Behav. Res. Monogr. 1967, 3:1-212.
16. Malinowski E.R. Determination of the number of factors and the experimental error in a data matrix. Anal. Chem. 1977, 49:612-617.
17. Krzanowski W.J., Kline P. Cross-validation for choosing the number of important components in principal component analysis. Multivar. Behav. Res. 1995, 30:149-165.
18. Kiers H.A.L. Weighted least squares fitting using iterative ordinary least squares algorithms. Psychometrika 1997, 62:251-266.
19. Gabrielsson J., Jonsson H., Trygg J., Airiau C., Schmidt B., Escott R. Combining process and spectroscopic data to improve batch modeling. AIChE J. 2006, 52:3164-3172. 10.1002/aic.10932.
20. Denham M.C., Brown P.J. Calibration with many variables. J. R. Stat. Soc. Ser. C 1993, 42:515-528.