Multi-way PLS for discrimination: Compact form equivalent to the tri-linear PLS2 procedure and its monotony convergence

Chemometrics and Intelligent Laboratory Systems

Volumn 133, Issue , 2014, Pages 25-32

  Ouertani, Samia Samar ^a   Mazerolles, Gérard ^c   Boccard, Julien ^b   Rudaz, Serge ^b   Hanafi, Mohamed ^a  

^a LUNAM UNIVERSITÉ   (France)

^b UNIVERSITY OF GENEVA   (Switzerland)

^c SPO   (France)

Author keywords

Discriminant analysis; Multi way PLS regression; Three way data; Tri linear PLS2

Indexed keywords

ALGORITHM; ARTICLE; CONTROLLED STUDY; DISCRIMINANT ANALYSIS; LINEAR SYSTEM; MATHEMATICAL COMPUTING; MATHEMATICS; MULTI WAY PARTIAL LEAST SQUARES REGRESSION; PARTIAL LEAST SQUARES REGRESSION; PRIORITY JOURNAL; SCORING SYSTEM; SIMULATION;

EID: 84896717230     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2014.01.015     Document Type: Article

References (25)

1. Wold S., Michael Sjostro M., Eriksson L. PLS-regression a basic tool of chemometrics. Chemometr. Intell. Lab. 2001, 58:109-130.
2. Barker M., Rayens W. Partial least squares for discrimination. J. Chemometr. 2003, 17:166-173.
3. Brooks R., Stone M. Joint continuum regression for multiple predictands. J. Am. Stat. Assoc. 1994, 89:1374-1377.
4. Indahl Ulf.G., Martens H., Naes T. From dummy regression to prior probabilities in PLSDA. J. Chemometr. 2007, 21:529-536.
5. Liland K.H., Indhal U.G. Powered partial least squares discriminant analysis. J. Chemometr. 2009, 23:7-18.
6. Nocairi H., Qannari E.M., Vigneau E., Bertrand D. Discrimination on latent components with respect to patterns. application to multicollinear data. Comput. Stat. Data Anal. 2005, 48:139-147.
7. Briandet R., Kemsley E., Wilson R. Discrimination of Arabica and robusta in instant coffee by Fourier transform infrared spectroscopy and chemometrics. J. Agric. Food Chem. 1996, 44:170-174.
8. Chevallier S., Bertrand D., Kohler A., Courcoux P. Application of PLS-DA in multivariate image analysis. J. Chemometr. 2006, 20:221-229.
9. Gotfries J., Blennow K., Walling A., Gottfries C.G. Diagnosis of dementias using partial least squares discriminant analysis. Dementia 1995, 6:83-88.
10. Louwerse D.J., Tates A.A., Smilde A.K., Koot G.L.M., Berndt H. PLS Discriminant Analysis with contribution plots to determine differences between parallel batch reactors in the process industry. Chemometr. Intell. Lab. 1999, 46:197-206.
11. Ortiz M., Sarabia L., Symington C., Santamaria F., Iniguez M. Analysis of ageing and typification of vintage ports by partial least squares and soft independent modelling class analogy. Analyst 1996, 121:1009-1013.
12. Shetty N., Olesen M.H., Gislum R., Deleuran L.C., Boelt B. Use of partial least squares discriminant analysis on visible-near infrared multispectral image data to examine germination ability and germ length in spinach seeds. J. Chemometr. 2011, 10:462-466.
13. Vong R., Geladi P., Wold S., Esbensen K. Source contributions to ambient aerosol calculated by discriminant partial least squares regression. J. Chemometr. 1998, 2:281-296.
14. Boccard J., Badoud F., Grata E., Ouertani S., Hanafi M., Mazerolles G., Lantéri P., Veuthey J.-L., Rudaz S. A steroidomic approach for biomarkers discovery in doping control. Forensic Sci. Int. 2011, 213:85-89.
15. Arancibia J.A., Boschetti C.E., Olivieri A.C., Escandar G.M. Screening of oil samples on the basis of excitation-emission room-temperature phosphorescence data and multiway chemometric techniques. Introducing the second-order advantage in a classification study. Anal. Chem. 2008, 80:2789-2798.
16. Castro C., Manetti C. A multiway approach to analyze metabonomic data: a study of maize seeds development. Anal. Bioanal. Chem. 2007, 371:194-200.
17. Hall G.J., Clow K., Kenny J.E. Estuarial fingerprinting through multidimensional fluorescence and multivariate analysis. Environ. Sci. Technol. 2005, 39:7560-7567.
18. Bro R. Multi-way calibration, multi-linear PLS. J. Chemometr. 1996, 10:47-62.
19. Smilde A.K. Comments on multilinear PLS. J. Chemom. 1997, 11:367-377.
20. Van Loan C.F. The ubiquitous Kronecker product. J. Comput. Appl. Math. 2000, 123:85-100.
21. De Lathauwer L., De Moor B., Vandewalle J. Multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 2000, 21:1253-1278.
22. Kolda T.G. Multilinear operators for higher-order decompositions. Tech. Report SAND2006-2081 2006, Sandia National Laboratories, Albuquerque, NM, Livermore, CA.
23. Kemsley E.K. Discriminant analysis of high-dimensional data: a comparison of principal components analysis and partial least squares data reduction methods. Chemometr. Intell. Lab. 1996, 33:47-61.
24. Andersson C.A., Bro R. The N-way toolbox for MATLAB. Chemometr. Intell. Lab. 2000, 52:1-4.
25. Sudhir R.G., Balmohan V.L. A Course in Calculus and Real Analysis 2010, Springer.