title: A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data.
abstract: Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.
authors.affiliation: Department of Chemistry, University of Newcastle, Callaghan, NSW 2308, Australia. Electronic address: azadeh.golshan@uon.edu.au.
authors.forename: Azadeh
authors.initials: A
authors.lastname: Golshan
authors.affiliation: Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran.
authors.forename: Hamid
authors.initials: H
authors.lastname: Abdollahi
authors.affiliation: Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran; Institute of Process Engineering, Faculty of Engineering, University of Szeged, H-6725 Szeged, Moszkvai krt. 5-7, Hungary.
authors.forename: Samira
authors.initials: S
authors.lastname: Beyramysoltan
authors.affiliation: Department of Chemistry, University of Newcastle, Callaghan, NSW 2308, Australia.
authors.forename: Marcel
authors.initials: M
authors.lastname: Maeder
authors.affiliation: Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany; Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Neymeyr
authors.affiliation: Institute of Process Engineering, Faculty of Engineering, University of Szeged, H-6725 Szeged, Moszkvai krt. 5-7, Hungary.
authors.forename: Robert
authors.initials: R
authors.lastname: Rajkó
authors.affiliation: Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
authors.forename: Mathias
authors.initials: M
authors.lastname: Sawall
authors.affiliation: IDAEA-CSIC, Jordi Girona 18-24, Barcelona 08034, Spain.
authors.forename: Romá
authors.initials: R
authors.lastname: Tauler
keywords: Band boundaries of feasible solutions; Rotational ambiguity; Soft modelling; Unique solutions