A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Azadeh Golshan; Hamid Abdollahi; Samira Beyramysoltan; Marcel Maeder; Klaus Neymeyr; Robert Rajkó; Mathias Sawall; Romá Tauler

doi:10.1016/j.aca.2016.01.011

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data

Anal Chim Acta. 2016 Mar 10:911:1-13. doi: 10.1016/j.aca.2016.01.011. Epub 2016 Jan 11.

Authors

Azadeh Golshan¹, Hamid Abdollahi², Samira Beyramysoltan³, Marcel Maeder⁴, Klaus Neymeyr⁵, Robert Rajkó⁶, Mathias Sawall⁷, Romá Tauler⁸

Affiliations

¹ Department of Chemistry, University of Newcastle, Callaghan, NSW 2308, Australia. Electronic address: azadeh.golshan@uon.edu.au.
² Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran.
³ 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.
⁴ Department of Chemistry, University of Newcastle, Callaghan, NSW 2308, Australia.
⁵ Leibniz-Institut für Katalyse, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany; Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
⁶ Institute of Process Engineering, Faculty of Engineering, University of Szeged, H-6725 Szeged, Moszkvai krt. 5-7, Hungary.
⁷ Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, 18057 Rostock, Germany.
⁸ IDAEA-CSIC, Jordi Girona 18-24, Barcelona 08034, Spain.

PMID: 26893081
DOI: 10.1016/j.aca.2016.01.011

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.

Keywords: Band boundaries of feasible solutions; Rotational ambiguity; Soft modelling; Unique solutions.

Publication types

Review