Maximum Likelihood Principal Component Analysis as initial projection step in Multivariate Curve Resolution analysis of noisy data

Chemometrics and Intelligent Laboratory Systems

Volumn 118, Issue , 2012, Pages 33-40

  Dadashi, Mahsa ^a,b   Abdollahi, Hamid ^b   Tauler, Romà ^a  

^a INSTITUTE OF ENVIRONMENTAL ASSESSMENT AND WATER RESEARCH   (Spain)

^b INSTITUTE FOR ADVANCED STUDIES IN BASIC SCIENCES IASBS   (Iran)

Author keywords

Alternating Least Squares; Error structure; Maximum Likelihood Principal Component Analysis; Multivariate Curve Resolution; Noisy data; Weighted Alternating Least Squares

Indexed keywords

ALGORITHM; ANALYTIC METHOD; ARTICLE; CONTROLLED STUDY; DATA ANALYSIS; ENVIRONMENTAL MONITORING; MAXIMUM LIKELIHOOD PRINCIPAL COMPONENT ANALYSIS MULTIVARIATE CURVE RESOLUTION ALTERNATING LEAST SQUARES; MULTIVARIATE CURVE RESOLUTION ALTERNATING LEAST SQUARES; MULTIVARIATE CURVE RESOLUTION WEIGHTED ALTERNATING LEAST SQUARES; NOISE; PRIORITY JOURNAL; SIMULATION;

EID: 84865278262     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2012.07.009     Document Type: Article

References (36)

1. Parastar H., Radović J.R., Jalali-Heravi M., Diez S., Bayona J.M., Tauler R. Resolution and Quantification of complex mixtures of polycyclic aromatic hydrocarbons in heavy fuel oil sample by means of GC-GC-TOFMS combined to multivariate curve resolution. Analytical Chemistry 2011, 83:9289-9297.
2. Terrado M., Barceló D., Tauler R. Quality assessment of the multivariate curve resolution alternating least squares (MCR-ALS) method for the investigation of environmental pollution patterns in surface water. Environmental Science and Technology 2009, 43:5321-5326.
3. Goicoichea H.C., Olivieri A.C., Tauler R. Application of the correlation constrained multivariate curve resolution alternating least-squares method for analyte quantitation in the presence of unexpected interferences using first-order instrumental data. Analyst 2010, 135:634-642.
4. Leger M.N., Vega-Montoto L., Wentzell P.D. Methods for systematic investigation of measurement error covariance matrices. Chemometrics and Intelligent Laborary Systems 2005, 77:181-205.
5. Kiers H.A.L. Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 1997, 62:251-266.
6. Simeon V., Pavkovic D. Weighted analysis of principal components: two approximations to statistical weights. Journal of Chemometrics 1992, 6:257-266.
7. Paatero P., Tapper U. Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 1994, 5:111-126.
8. Wentzell P.D., Andrews D.T., Hamilton D.C., Faber K., Kowalski B.R. Maximum likelihood principal component analysis. Journal of Chemometrics 1997, 11:339-366.
9. Wentzell P.D., Andrews D.T., Kowalski B.R. Maximum likelihood multivariate calibration. Analytical Chemistry 1997, 69:2299-2311.
10. Vega-Montoto L., Wentzell P.D. Maximum likelihood parallel factor analysis (MLPARAFAC). Journal of Chemometrics 2003, 17:237-253.
11. Wentzell P.D., Karakach T.K., Roy S., Martinez M.J., Allen C.P., Werner-Washburne M. Multivariate curve resolution of time course microarray data. BMC Bioinformatics 2006, 7:343.
12. Jaumot J., Pina B., Tauler R. Application of MCR methods to the analysis of yeast genome-wide screens. Chemometrics and Intelligent Laborary Systems 2010, 104:53-64.
13. Tauler R., Viana M., Querol X., Alastuey A., Flight R.M., Wentzell P.D., Hopke P.K. Comparison of the results obtained by four receptor modelling methods in aerosol source apportionment studies. Atmospheric Environment 2009, 43:3989-3997.
14. Stanimirova I., Tauler R., Walczak B. A comparison of positive matrix factorization and the weighted multivariate curve resolution method. Application to environmental data. Environmental Science and Technology 2011, 45:10102-10110.
15. Tauler R. Multivariate curve resolution applied to second order data. Chemometrics and Intelligent Laborary Systems 1995, 30:133-146.
16. Tauler R., Smilde A., Kowalski B. Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution. Journal of Chemometrics 1995, 9:31-58.
17. Jaumot J., Gargallo R., de Juan A., Tauler R. A graphical user friendly interface for MCR-ALS: a new tool for Multivariate Curve Resolution in MATLAB. Chemometrics and Intelligent Laborary Systems 2005, 76:101-110.
18. Wold S., Esbensen K., Geladi P. Principal component analysis. Chemometrics and Intelligent Laborary Systems 1987, 2:37-52.
19. Wentzell P.D. Other topics in soft-modeling: maximum likelihood-based soft-modeling methods. Comprehensive Chemometrics 2009, vol. 2:507-558. Elsevier, Oxford. S. Brown, R. Tauler, B. Walczak (Eds.).
20. Wentzell P.D., Lohnes M.T. Maximum likelihood principal component analysis with correlated measurement errors: theoretical and practical considerations. Chemometrics and Intelligent Laborary Systems 1999, 45:65-85.
21. De Juan A., Van der Heyden Y., Tauler R., Massart D.L. Assessment of new constraints applied to the alternating least squares method. Analytica Chimica Acta 1997, 346:307-318.
22. Bro R., De Jong S. A fast non-negativity-constrained least squares algorithm. Journal of Chemometrics 1997, 11:393-401.
23. Tauler R. Application of non-linear optimization methods to the estimation of multivariate curve resolution solutions and of their feasible band boundaries in the investigation of two chemical and environmental simulated data sets. Analytica Chimica Acta 2007, 595:289-298.
24. Smilde A.K., Kiers H.A.L., Bijlsma S., Rubingh C.M., van Erk M.J. Matrix correlations for high-dimensional data: the modified RV-coefficient. Bioinformatics 2009, 25:401-405.
25. Bjorck A., Golub G. Numerical methods for computing angles between linear subspaces. Mathematics of Computation 1973, 27:579-594.
26. Wedin P.-A. On angles between subspaces of a finite dimensional inner product space. Lecture Notes in Mathematics 1983, 973:263-285. Springer. B. Kagstrom, A. Ruhe (Eds.).
27. Windig W., Guilment J. Interactive self-modeling mixture analysis. Analytical Chemistry 1991, 63:1425-1432.
28. Lawton W.H., Sylvestre E.A. Self modeling curve resolution. Technometrics 1969, 13:617-633.
29. Abdollahi H., Maeder M., Tauler R. Calculation and meaning of feasible band boundaries in multivariate curve resolution of a two-component system. Analytical Chemistry 2009, 81:2115-2122.
30. Tauler R. Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution. Journal of Chemometrics 2001, 15:627-646.
31. Abdollahi H., Tauler R. Uniqueness and rotation ambiguities in multivariate curve resolution methods. Chemometrics and Intelligent Laborary Systems 2011, 108:100-111.
32. Jaumot J., Tauler R. MCR-BANDS: a user friendly MATLAB program for the evaluation of rotation ambiguities in Multivariate Curve Resolution. Chemometrics and Intelligent Laborary Systems 2010, 103:96-107.
33. Mason C., Maeder M., Whitson A. Resolving factor analysis. Analytical Chemistry 2001, 73:1587-1594.
34. Gemperline P.J. A priori estimates of the elution profiles of the pure components in overlapped liquid chromatography peaks using target factor analysis. Journal of Chemical Information and Computer Sciences 1984, 24:206-212.
35. Maeder M., Zuberbühler A.D. Nonlinear least-squares fitting of multivariate absorption data. Analytical Chemistry 1990, 62:2220-2224.
36. De Juan A., Maeder M., Martinez M., Tauler R. Combining hard- and soft-modelling to solve kinetic problems. Chemometrics and Intelligent Laborary Systems 2000, 54:123-141.