Concept and role of extreme objects in PCA/SIMCA

Journal of Chemometrics

Volumn 28, Issue 5, 2014, Pages 429-438

  Pomerantsev, Alexey L ^a,b   Rodionova, Oxana Ye ^a  

^a SEMENOV INSTITUTE OF CHEMICAL PHYSICS   (Russian Federation)

^b Institute of Natural and Technical Systems RAS   (Russian Federation)

Author keywords

Chi squared distribution; Extreme samples; Outliers; PCA; Robust methods; Scores and orthogonal distances; SIMCA; Thresholds; Tolerance areas

Indexed keywords

CALIBRATION; DATA HANDLING; DEGREES OF FREEDOM (MECHANICS); METHOD OF MOMENTS; PROBABILITY DISTRIBUTIONS; STATISTICS;

CHI-SQUARED DISTRIBUTION; EXTREME SAMPLE; INDEPENDENT MODEL; OUTLIER; PRINCIPAL-COMPONENT ANALYSIS; ROBUST METHODS; SCORE AND ORTHOGONAL DISTANCE; SOFT INDEPENDENT MODELING BY CLASS ANALOGY; THRESHOLD; TOLERANCE AREA;

PRINCIPAL COMPONENT ANALYSIS;

EID: 84900315224     PISSN: 08869383     EISSN: 1099128X     Source Type: Journal    
DOI: 10.1002/cem.2506     Document Type: Article

References (25)

1. Pomerantsev AL, Rodionova OY. Chemometric view on "comprehensive chemometrics". Chemom. Intell. Lab. Syst. 2010; 103: 19-24.
2. Huber PJ. Robust Statistics. John Wiley & Sons: Chichester, 1981.
3. Tax D, Duin R. Outlier detection using classifier instability. Lect. notes Comput. Sci. 1998; 1451: 593-601.
4. Rodionova OY, Sokovikov YV, Pomerantsev AL. Quality control of packed raw materials in pharmaceutical industry. Anal. Chim. Acta 2009; 642: 222-227.
5. Rodionova OY, Pomerantsev AL. NIR based approach to counterfeit-drug detection. Trends Anal. Chem. 2010; 29: 781-938.
6. Rodionova OY, Pomerantsev AL, Simple view on simple interval calculation (SIC) method. Chemom. Intell. Lab. Syst. 2009; 97: 64-76.
7. Filzmoser P, Serneels S, Maronna R, Van Espen PJ. Robust multivariate methods in chemometrics. In Comprehensive Chemometrics. Chemical and Biochemical Data Analysis. Editors-in-Chief: Brown Stephen D, Tauler Romà, Walczak Beata (eds.). Elsevier: Amsterdam, 2009, 4 volumes.
8. Box GEP. Some theorems on quadratic forms applied in the study of analysis of variance problems: I. Effect of inequality of variance in one-way classification. Ann. Math. Statist. 1954; 25: 290-302.
9. Maronna RA, Martin RD, Yohai VJ. Robust Statistics. Theory and Methods. Wiley: Toronto, 2006.
10. Locantore N, Marron JS, Simpson DG, Tripoli N, Zhang JT, Cohen KL. Principal component analysis for functional data. Test 1999; 8: 1-73.
11. Daszykowski M, Kaczmarek K, Vander Heyden Y, Walczak B. Robust statistics in data analysis-a review: basic concepts. Chemom. Intell. Lab. Syst. 2007; 85: 203-219.
12. Hubert M, Rousseeuw PJ, Vanden Branden K. ROBPCA: a new approach to robust principal component analysis. Technometrics 2005; 47: 64-79.
13. Daszykowski M, Kaczmarek K, Stanimirova I, Vander Heyden Y, Walczak B. Robust SIMCA-bounding influence of outliers. Chemom. Intell. Lab. Syst. 2007; 87: 95-103.
14. Pomerantsev A. Acceptance areas for multivariate classification derived by projection methods. J. Chemometrics 2008; 22: 601-609.
15. Kowalski BR, Wold S. Pattern recognition in chemistry. In Handbook of Statistics, 2. Krishnaiah PR, Kanal LN (eds.). North-Holland Publishing Company 1982, 673-697.
16. De Maesschalck R, Jouan-Rimbaud D, Massart DL. Tutorial. The Mahalanobis distance. Chemom. Intell. Lab. Syst. 2000; 50: 1-18.
17. Satterthwaite FE. Synthesis of variance. Psychometrika 1941; 6: 309-316.
18. Ali MM, Obaidullah M. Distribution of linear combinations of exponential variates. Commun Stat Theor 1982; 11: 1453-1463.
19. Wood ATA. An F approximation to the distribution of a linear combination of chi-squared variables. Commun Stat Simulat 1989; 18: 1439-1456.
20. Bentler PM, Xie J. Corrections to test statistics in principal Hessian directions. Stat. Probabil. Lett 2000; 47: 381-389.
21. Croux C, Ruiz-Gazen A. High breakdown estimators for principal components: the projection-pursuit approach revisited. J Multivariate Anal 2005; 95: 206-226.
22. ROBPCA. Robust principal component analysis based on the projection-pursuit approach http://www.econ.kuleuven.be/public/NDBAE06/programs/pca/robpca.txt
23. Nomikos P, MacGregor JF. Multivariate SPC charts for monitoring batch processes. Technometrics 1995; 37: 41-59.
24. Vanden Branden K, Hubert M. Robust classification in high dimensions based on the SIMCA method. Chemom. Intell. Lab. Syst 2005; 79: 10-21.
25. Héberger K, Kollár-Hunek K. Sum of ranking differences for method discrimination and its validation: comparison of ranks with random numbers. J. Chemometrics 2011; 25: 151-158.