Natural duality in minimal constrained self modeling curve resolution

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

Self modeling curve resolution (SMCR) was introduced by Lawton and Sylvestre (LS) [Technometrics 1971; 13: 617-633] to decompose raw spectroscopic data of two component systems into product of two physically interpretable profile matrices provided that both concentrations and absorbances are non-negative, accepting both as minimal constraints. Later Borgen et al. in 1985-86 [Anal. Chim. Acta 1985; 174: 1-26; Microchim. Acta 1986; 11: 63-73] generalized LS method for three-component systems with the same minimal constraints. The concepts of Borgen were rather difficult to understand and to implement, that is why several chemometricians turned to developing approximation methods. Very recently, Rajkó and István [J. Chemom. 2005; 19: 448-463] have revisited Borgen's method and they have given clearer interpretation and used computational geometry tools to find inner and outer polygons. In the meantime Henry [Chemom. Intell. Lab. Syst. 2005; 77: 59-63] has introduced the duality relationship, but he has described it only for multivariate receptor modeling of compositional data of airborne pollution. Generalization of his duality principle will be given in this paper for universally using it in SMCR which is based on singular value decomposition (SVD) or principal component analysis (PCA).

Original languageEnglish
Pages (from-to)164-169
Number of pages6
JournalJournal of Chemometrics
Volume20
Issue number3-4
DOIs
Publication statusPublished - Mar 2006

Fingerprint

Curve Resolution
Natural Duality
Computational geometry
Singular value decomposition
Principal component analysis
Pollution
Modeling
Compositional Data
Duality Principle
Henry
Computational Geometry
Approximation Methods
Receptor
Principal Component Analysis
Polygon
Duality
Non-negative
Decompose

Keywords

  • Bilinear spectroscopic data
  • Borgen plot
  • Chemometrics
  • Duality
  • Principal component analysis (PCA)
  • Self-modeling curve resolution (SMCR)
  • Singular value decomposition (SVD)

ASJC Scopus subject areas

  • Analytical Chemistry
  • Statistics and Probability

Cite this

Natural duality in minimal constrained self modeling curve resolution. / Rajkó, R.

In: Journal of Chemometrics, Vol. 20, No. 3-4, 03.2006, p. 164-169.

Research output: Contribution to journalArticle

@article{050f603d0f914ee49b91c564670a871a,
title = "Natural duality in minimal constrained self modeling curve resolution",
abstract = "Self modeling curve resolution (SMCR) was introduced by Lawton and Sylvestre (LS) [Technometrics 1971; 13: 617-633] to decompose raw spectroscopic data of two component systems into product of two physically interpretable profile matrices provided that both concentrations and absorbances are non-negative, accepting both as minimal constraints. Later Borgen et al. in 1985-86 [Anal. Chim. Acta 1985; 174: 1-26; Microchim. Acta 1986; 11: 63-73] generalized LS method for three-component systems with the same minimal constraints. The concepts of Borgen were rather difficult to understand and to implement, that is why several chemometricians turned to developing approximation methods. Very recently, Rajk{\'o} and Istv{\'a}n [J. Chemom. 2005; 19: 448-463] have revisited Borgen's method and they have given clearer interpretation and used computational geometry tools to find inner and outer polygons. In the meantime Henry [Chemom. Intell. Lab. Syst. 2005; 77: 59-63] has introduced the duality relationship, but he has described it only for multivariate receptor modeling of compositional data of airborne pollution. Generalization of his duality principle will be given in this paper for universally using it in SMCR which is based on singular value decomposition (SVD) or principal component analysis (PCA).",
keywords = "Bilinear spectroscopic data, Borgen plot, Chemometrics, Duality, Principal component analysis (PCA), Self-modeling curve resolution (SMCR), Singular value decomposition (SVD)",
author = "R. Rajk{\'o}",
year = "2006",
month = "3",
doi = "10.1002/cem.999",
language = "English",
volume = "20",
pages = "164--169",
journal = "Journal of Chemometrics",
issn = "0886-9383",
publisher = "John Wiley and Sons Ltd",
number = "3-4",

}

TY - JOUR

T1 - Natural duality in minimal constrained self modeling curve resolution

AU - Rajkó, R.

PY - 2006/3

Y1 - 2006/3

N2 - Self modeling curve resolution (SMCR) was introduced by Lawton and Sylvestre (LS) [Technometrics 1971; 13: 617-633] to decompose raw spectroscopic data of two component systems into product of two physically interpretable profile matrices provided that both concentrations and absorbances are non-negative, accepting both as minimal constraints. Later Borgen et al. in 1985-86 [Anal. Chim. Acta 1985; 174: 1-26; Microchim. Acta 1986; 11: 63-73] generalized LS method for three-component systems with the same minimal constraints. The concepts of Borgen were rather difficult to understand and to implement, that is why several chemometricians turned to developing approximation methods. Very recently, Rajkó and István [J. Chemom. 2005; 19: 448-463] have revisited Borgen's method and they have given clearer interpretation and used computational geometry tools to find inner and outer polygons. In the meantime Henry [Chemom. Intell. Lab. Syst. 2005; 77: 59-63] has introduced the duality relationship, but he has described it only for multivariate receptor modeling of compositional data of airborne pollution. Generalization of his duality principle will be given in this paper for universally using it in SMCR which is based on singular value decomposition (SVD) or principal component analysis (PCA).

AB - Self modeling curve resolution (SMCR) was introduced by Lawton and Sylvestre (LS) [Technometrics 1971; 13: 617-633] to decompose raw spectroscopic data of two component systems into product of two physically interpretable profile matrices provided that both concentrations and absorbances are non-negative, accepting both as minimal constraints. Later Borgen et al. in 1985-86 [Anal. Chim. Acta 1985; 174: 1-26; Microchim. Acta 1986; 11: 63-73] generalized LS method for three-component systems with the same minimal constraints. The concepts of Borgen were rather difficult to understand and to implement, that is why several chemometricians turned to developing approximation methods. Very recently, Rajkó and István [J. Chemom. 2005; 19: 448-463] have revisited Borgen's method and they have given clearer interpretation and used computational geometry tools to find inner and outer polygons. In the meantime Henry [Chemom. Intell. Lab. Syst. 2005; 77: 59-63] has introduced the duality relationship, but he has described it only for multivariate receptor modeling of compositional data of airborne pollution. Generalization of his duality principle will be given in this paper for universally using it in SMCR which is based on singular value decomposition (SVD) or principal component analysis (PCA).

KW - Bilinear spectroscopic data

KW - Borgen plot

KW - Chemometrics

KW - Duality

KW - Principal component analysis (PCA)

KW - Self-modeling curve resolution (SMCR)

KW - Singular value decomposition (SVD)

UR - http://www.scopus.com/inward/record.url?scp=34247271407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247271407&partnerID=8YFLogxK

U2 - 10.1002/cem.999

DO - 10.1002/cem.999

M3 - Article

AN - SCOPUS:34247271407

VL - 20

SP - 164

EP - 169

JO - Journal of Chemometrics

JF - Journal of Chemometrics

SN - 0886-9383

IS - 3-4

ER -