Does the signal contribution function attain its extrema on the boundary of the area of feasible solutions?
The signal contribution function (SCF) was introduced by Gemperline in 1999 and Tauler in 2001 in order to study band boundaries of multivariate curve resolution (MCR) methods. In 2010 Rajkó pointed out that the extremal profiles of the SCF reproduce the limiting profiles of the Lawton-Sylvestre plo...
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| Published in: | Chemometrics and intelligent laboratory systems Vol. 196; p. 103887 |
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| Abstract | The signal contribution function (SCF) was introduced by Gemperline in 1999 and Tauler in 2001 in order to study band boundaries of multivariate curve resolution (MCR) methods. In 2010 Rajkó pointed out that the extremal profiles of the SCF reproduce the limiting profiles of the Lawton-Sylvestre plots for the case of noise-free two-component systems.
This paper mathematically investigates two-component systems and includes a self-contained proof of the SCF-boundary property for two-component systems. It also answers the question if a comparable behavior of the SCF still holds for chemical systems with three components or even more components with respect to their area of feasible solutions. A negative answer is given by presenting a noise-free three-component system for which one of the profiles maximizing the SCF is represented by a point in the interior of the associated area of feasible solutions.
•The signal contribution function (SCF) is a powerful tool for the analysis of band boundaries in MCR computations.•For two-component systems a self-contained proof shows that SCF extrema are taken on the boundary of the Lawton-Sylvestre cone.•A three-component system is analyzed for which the SCF attains one maximum in the interior of the area of feasible solutions. |
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| AbstractList | The signal contribution function (SCF) was introduced by Gemperline in 1999 and Tauler in 2001 in order to study band boundaries of multivariate curve resolution (MCR) methods. In 2010 Rajkó pointed out that the extremal profiles of the SCF reproduce the limiting profiles of the Lawton-Sylvestre plots for the case of noise-free two-component systems.
This paper mathematically investigates two-component systems and includes a self-contained proof of the SCF-boundary property for two-component systems. It also answers the question if a comparable behavior of the SCF still holds for chemical systems with three components or even more components with respect to their area of feasible solutions. A negative answer is given by presenting a noise-free three-component system for which one of the profiles maximizing the SCF is represented by a point in the interior of the associated area of feasible solutions.
•The signal contribution function (SCF) is a powerful tool for the analysis of band boundaries in MCR computations.•For two-component systems a self-contained proof shows that SCF extrema are taken on the boundary of the Lawton-Sylvestre cone.•A three-component system is analyzed for which the SCF attains one maximum in the interior of the area of feasible solutions. |
| ArticleNumber | 103887 |
| Author | Tauler, Romà Golshan, Azadeh Neymeyr, Klaus Sawall, Mathias Engel, Konrad |
| Author_xml | – sequence: 1 givenname: Klaus surname: Neymeyr fullname: Neymeyr, Klaus email: klaus.neymeyr@uni-rostock.de organization: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057, Rostock, Germany – sequence: 2 givenname: Azadeh surname: Golshan fullname: Golshan, Azadeh organization: University of Newcastle, Department of Chemistry, Callaghan, NSW, 2308, Australia – sequence: 3 givenname: Konrad surname: Engel fullname: Engel, Konrad organization: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057, Rostock, Germany – sequence: 4 givenname: Romà surname: Tauler fullname: Tauler, Romà organization: Institute of Environmental Assessment and Water Research, Spanish Council of Research, Jordi Girona 18, 08034, Barcelona, Spain – sequence: 5 givenname: Mathias surname: Sawall fullname: Sawall, Mathias organization: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057, Rostock, Germany |
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| CitedBy_id | crossref_primary_10_1016_j_chemolab_2021_104472 crossref_primary_10_1016_j_chemolab_2021_104387 crossref_primary_10_1016_j_aca_2023_341354 crossref_primary_10_1021_acs_analchem_0c01395 crossref_primary_10_1016_j_chemolab_2023_104901 crossref_primary_10_1016_j_chemolab_2022_104636 crossref_primary_10_1002_cem_3317 crossref_primary_10_1016_j_aca_2020_10_051 crossref_primary_10_1002_cem_3535 crossref_primary_10_1002_cem_3363 crossref_primary_10_1016_j_aca_2021_338206 crossref_primary_10_1016_j_chemolab_2023_105033 crossref_primary_10_1016_j_microc_2020_105615 |
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| Title | Does the signal contribution function attain its extrema on the boundary of the area of feasible solutions? |
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