Shifted factor analysis - Part III: N-way generalization and application

Journal of Chemometrics

Volumn 17, Issue 7, 2003, Pages 389-399

  Hong, Sungjin ^a   Harshman, Richard A ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Chromatography; Lag; Latent position shift; Latent variable models; Multilinearity; Multiway analysis; Parafac1; Parafac2; Quasi ALS; Shifted factor analysis

Indexed keywords

CHROMATOGRAPHY; MULTIVARIANT ANALYSIS;

FACTORS ANALYSIS; LAG; LATENT POSITION SHIFT; LATENT VARIABLE MODELING; MULTILINEARITY; MULTIWAY ANALYSIS; PARAFAC1; PARAFAC2; QUASI-ALS; SHIFTED FACTOR ANALYSE;

FACTOR ANALYSIS;

ALGORITHM; ARTICLE; CHEMOMETRIC ANALYSIS; CHROMATOGRAPHY; DATA ANALYSIS; FACTORIAL ANALYSIS; MATHEMATICAL MODEL;

EID: 0142011494     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/cem.810     Document Type: Article

References (32)

1. Field AS, Graupe D. Topographic component (parallel factor) analysis of multichannel evoked potentials: practical issues in trilinear spatiotemporal decomposition. Brain Topogr. 1991; 3: 407-423.
2. Bro R, Anderson CA, Kiers HAL. PARAFAC2 - Part II. Modeling chromatographic data with retention time shifts. J. Chemometrics 1999; 13: 295-309.
3. Tauler R. Multivariate curve resolution applied to second order data. Chemometrics Intell. Lab. Syst. 1995; 30: 133-146.
4. Harshman RA, Hong S, Lundy ME. Shifted factor analysis. Part I. Models and properties. J. Chemometrics 2003; 17: 363-378.
5. Hong S, Harshman RA. Shifted factor analysis. Part II. Algorithms. J. Chemometrics 2003; 17: 379-388.
6. Bro R. Multi-way Analysis in the Food Industry: Models, Algorithms and Applications. University of Amsterdam: Amsterdam, 1998. (http://www.models.kvl.dk/users//asmus/thesis/thesis.html).
7. Kiers HAL, ten Berge JMF, Bro R. PARAFAC2 - Part I. A direct fitting algorithm for the PARAFAC2 model. J. Chemometrics 1999; 13: 275-294.
8. Harshman RA. PARAFAC2: mathematical and technical notes. UCLA Working Papers Phonet. 1972; 22: 30-44. (http://publish.uwo.ca/~harshman/wpppfac2.pdf).
9. Harshman RA. An index formalism that generalizes the capabilities of matrix notation and algebra to n-way arrays. J. Chemometrics 2001; 15: 689-714.
10. Hong S. Shifted factor analysis: a test of models and algorithms. Master's Thesis, University of Western Ontario, London, ON, 1997.
11. Carroll JD, Chang JJ. Analysis of individual differences in multidimensional scaling via N-way generalization of 'Eckart-Young' decomposition. Psychometrika 1970; 35: 283-319.
12. Harshman RA. Foundations of the PARAFAC procedure: models and conditions for an 'explanatory' multi-modal factor analysis. UCLA Working Papers Phonet. 1970; 16: 1-84. (http://publish.uwo.ca/~harshman/wpppfac0.pdf).
13. Harshman RA, Hong S. 'Stretch' vs. 'slice' methods for representing three-way structure via matrix notation. J. Chemometrics 2002; 16: 198-205.
14. Harshman RA. Shifted factor analysis models and estimation expressed in array notation. Department of Psychology Res. Bull. #762, University of Western Ontario, London, ON, 2001. (http://publish.uwo.ca/~harshman).
15. Khatri CG, Rao CR. Solutions to some functional equations and their applications to characterization of probability distributions. Sankhya, Ser. A 1968; 30: 167-180.
16. Bro R, de Jong S. A fast non-negativity-constrained linear least squares algorithm for use in multi-way algorithms. J. Chemometrics 1997; 11: 393-401.
17. Kruskal JB, Harshman RA, Lundy ME. How 3-MFA data can cause degenerate PARAFAC solutions, among other relationships. In Multiway Data Analysis, Coppi R, Bolasco S (eds). Elsevier: Amsterdam, 1989; 115-122.
18. Lundy ME, Harshman RA, Kruskal JB. A two-stage procedure incorporating good features of both trilinear and quadrilinear models. In Multiway Data Analysis, Coppi R, Bolasco S (eds). Elsevier: Amsterdam, 1989; 123-130. (http://publish.uwo.ca/~harshman/pfcore89.pdf).
19. Paatero P. Construction and analysis of degenerate PARAFAC models. J. Chemometrics 2000; 14: 285-299.
20. Mitchell BC, Burdick DS. Slowly converging PARAFAC sequences: swamps and two-factor degeneracies. J. Chemometrics 1994; 8: 155-168.
21. Tucker LR. Some mathematical notes on three-mode factor analysis. Psychometrika 1966; 31: 279-311.
22. Kroonenberg PM. Three-mode Principal Component Analysis: Theory and Applications. DSWO Press: Leiden, 1983.
23. Kiers HAL. Weighted least squares fitting using ordinary least squares algorithms. Psychometrika 1997; 62: 251-266.
24. Kruskal JB. Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra Appl. 1977; 18: 95-138.
25. Cattell RB. The structuring of change by P-technique and incremental R-technique. In Problems in Measuring Change, Harris CW (ed.). University of Wisconsin Press: Madison, WI, 1963; 167-198.
26. Nielsen N-PV, Carstensen JM, Smedsgaard J. Aligning of single and multiple wavelength chromatographic profiles for chemometric data analysis using correlation optimized warping. J. Chromatogr. A 1998; 805: 17-35.
27. Bylund D, Danielsson R, Malmquist G, Markides KE. Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modeling of liquid chromatography-mass spectrometry data. J. Chromatogr. A 2002; 961: 237-244.
28. Westad F, Martens H. Shift and intensity modeling in spectroscopy - general concept and applications. Chemometrics Intell. Lab. Syst. 1999; 45: 361-370.
29. Horn BKP, Schunck BG. Determining optical flow. Artific. Intell. 1981; 17: 185-203.
30. Prazen BJ, Synovec RE, Kowalski BR. Standardization of second-order chromatographic/spectroscopic data for optimum chemical analysis. Anal. Chem. 1998; 70: 218-225.
31. Fraga CG, Prazen BJ, Synovec RE. Comprehensive two-dimensional gas chromatography and chemometrics for the high-speed quantitative analysis of aromatic isomers in a jet fuel using the standard addition method and an objective retention time alignment algorithm. Anal. Chem. 2000; 72: 4154-4162.
32. Vogels JTWE, Tas AC, Venekamp J, Van Der Greef J. Partial linear fit: a new NMR spectroscopy preprocessing tool for pattern recognition applications. J. Chemometrics 1996; 10: 425-438.