Generalization of rank reduction problems with Wedderburn's formula

Journal of Chemometrics

Volumn 17, Issue 11, 2003, Pages 603-607

  Ferré, Joan ^a   Faber, Nicolaas M ^b  

^a UNIVERSITAT ROVIRA I VIRGILI   (Spain)

^b Chemometry Consultancy   (Netherlands)

Author keywords

Multivariate calibration; Net analyte signal; Rank reduction; Wedderburn's formula

Indexed keywords

CALIBRATION METHOD; FIRST ORDER; GENERALISATION; MULTIVARIATE CALIBRATION; NET ANALYTE SIGNALS; RANK-REDUCTION; REDUCTION PROBLEM; SECOND-ORDER CALIBRATION; SPECTROSCOPIC DATA; WEDDERBURN FORMULA;

CALIBRATION;

ARTICLE; CALCULATION; CALIBRATION; CHEMOMETRICS; MATHEMATICAL ANALYSIS; MODEL; THEORY;

EID: 1042279679     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/cem.828     Document Type: Article

References (35)

1. Lorber A. Error propagation and figures of merit for quantification by solving matrix equations. Anal. Chem. 1986; 58: 1167-1172.
2. Lorber A, Kowalski BR. The effect of interferences and calibration design on accuracy: implications for sensor and sample selection. J. Chemometrics 1988; 2: 67-79.
3. Booksh KS, Kowalski BR. Theory of analytical chemistry. Anal. Chem. 1994; 66: 782A-791A.
4. Lorber A, Faber K, Kowalski BR. Net analyte signal calculation in multivariate calibration. Anal. Chem. 1997; 69: 1620-1626.
5. Faber K, Lorber A, Kowalski BR. Analytical figures of merit for tensorial calibration. J. Chemometrics 1997; 11: 419-461.
6. Faber NM. Multivariate sensitivity for the interpretation of the effect of spectral pretreatment methods on near-infrared calibration model predictions. Anal. Chem. 1999; 71: 557-565.
7. Goicoechea HC, Olivieri AC. Enhanced synchronous spectrofluorometric determination of tetracycline in blood serum by chemometric analysis. Comparison of partial least-squares and hybrid linear analysis calibrations. Anal. Chem. 1999; 71: 4361-4368.
8. Boqué R, Faber NM, Rius FX. Detection limits in classical multivariate calibration. Anal. Chim. Acta 2000; 43: 41-49.
9. Xu L, Schechter I. Wavelength selection for simultaneous spectroscopic analysis. Experimental and theoretical study. Anal. Chem. 1996; 68: 2392-2400.
10. Ferré J, Rius FX. Detection and correction of biased results of individual analytes in multicomponent spectroscopic analysis. Anal. Chem. 1998; 70: 1999-2007.
11. Goicoechea HC, Olivieri AC. Wavelength selection by net analyte signals calculated with multivariate factor-based hybrid linear analysis (HLA). A theoretical and experimental comparison with partial least-squares (PLS). Analyst 1999; 124: 725-731.
12. Wentzell PD, Andrews DT, Kowalski BR. Maximum likelihood multivariate calibration. Anal. Chem. 1997; 69: 2299-2311.
13. Shaffer RE, Combs R. Comparison of spectral and interferogram processing methods using simulated passive Fourier transform infrared remote sensing data. J. Appl. Spectrosc. 2001; 55: 1404-1413.
14. Faber NM. Exact presentation of multivariate calibration model as univariate calibration graph. Chemometrics Intell. Lab. Syst. 2000; 50: 107-114.
15. Berger AJ, Koo TW, Itzkan I, Feld MS. An enhanced algorithm for linear multivariate calibration. Anal. Chem. 1998; 70: 623-627.
16. Xu L, Schechter I. A calibration method free of optimal factor number selection for automated multivariate analysis. Experimental and theoretical study. Anal. Chem. 1997; 69: 3722-3730.
17. Park KS, Jun CH. Hybrid linear analysis based on the net analyte signal in spectral responses with orthogonal signal correction. Near Infrared Anal. 2000; 1: 1-8.
18. Goicoechea HC, Olivieri AC. Sustained prediction ability of net analyte preprocessing methods using reduced calibration sets. Theoretical and experimental study involving the spectrophotometric analysis of multicomponent mixtures. Analyst 2001; 126: 1105-1112.
19. Rodriguez D, Boschetti CE, Olivieri AC. Near-infrared spectroscopic determination of antioxidants and organic acids in rubbers assisted by a new multivariate calibration method based on direct orthogonalization. Analyst 2002; 127: 304-309.
20. Goicoechea HC, Olivieri AC. A comparison of orthogonal signal correction and net analyte preprocessing methods. Theoretical and experimental study. Chemometrics Intell. Lab. Syst. 2001; 56: 73-81.
21. Ferré J, Faber NM. Net analyte signal calculation for multivariate calibration. Chemometrics Intell. Lab. Syst. 2003; 69: 123-136.
22. Wedderburn JHM. Lectures on Matrices, vol. XVII of Colloquium Publications. American Mathematical Society: New York, 1934.
23. Ho CN, Christian GD, Davidson ER. Application of the method of rank annihilation to quantitative analyses of multicomponent fluorescence data from the video fluorometer. Anal. Chem. 1978; 50: 1108-1113.
24. Faber NM. Efficient computation of net analyte signal vector in inverse multivariate calibration models. Anal. Chem. 1998; 70: 5108-5110.
25. Bro R, Andersen CM. Theory of net analyte signal vectors in inverse regression. J. Chemometrics 2003; Submitted.
26. Bro R, Smilde AK. Centering and scaling in component analysis. J. Chemometrics 2003; 17: 16-33.
27. McCue M, Malinowski ER. Rank annihilation factor analysis of unresolved LC peaks. J. Chromatogr. Sci. 1983; 21: 229-234.
28. Lorber A. Quantifying chemical composition from two-dimensional data arrays. Anal. Chim. Acta 1984; 164: 293-297.
29. Sanchez E, Kowalski BR. Tensorial resolution: a direct trilinear decomposition. J. Chemometrics 1990; 4: 29-45.
30. Ferré J, Brown SD, Rius FX. Improved calculation of the net analyte signal in multivariate calibration J. Chemometrics 2001; 15: 537-553.
31. Lorber A, Wangen LE, Kowalski BR. A theoretical foundation for the PLS algorithm J. Chemometrics 1987; 1: 19-31.
32. Lorber A, Kowalski BR. Estimation of prediction error for multivariate calibration. J. Chemometrics 1988; 2: 93-109.
33. Andersson CA. Direct orthogonalization. Chemometrics Intell. Lab. Syst. 1999; 47: 51-63.
34. Fearn T. On orthogonal signal correction. Chemometrics Intell. Lab. Syst. 2000; 50: 47-52.
35. Svenson O, Kourti T, McGregor JF. An investigation of orthogonal signal correction algorithms and their characteristics. J. Chemometrics 2002; 16: 176-188.