Does the signal contribution function attain its extrema on the boundary of the area of feasible solutions?

• Published in: Chemometrics and intelligent laboratory systems Vol. 196; p. 103887
• Main Authors: Neymeyr, Klaus, Golshan, Azadeh, Engel, Konrad, Tauler, Romà, Sawall, Mathias
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15-01-2020
• Subjects: Area of feasible solutions; Borgen plot; FACPACK; Lawton-Sylvestre plot; MCR-Bands; Multivariate curve resolution; signal contribution function; MCR-Bands; Borgen plot; FACPACK; Multivariate curve resolution; Area of feasible solutions; signal contribution function; Lawton-Sylvestre plot
• ISSN: 0169-7439; 1873-3239
• DOI: 10.1016/j.chemolab.2019.103887

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.