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A general rule for uniqueness in self‐modeling curve resolution methods
Author(s) -
Karimvand Somaiyeh Khodadadi,
Lakeh Mahsa Akbari,
Tavakkoli Elnaz,
Ghaffari Mahdiyeh,
Omidikia Nematollah,
Abad Saeed Khalili Ali,
Rajkó Róbert,
Abdollahi Hamid
Publication year - 2020
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.3268
Subject(s) - chemometrics , uniqueness , resolution (logic) , computer science , a priori and a posteriori , field (mathematics) , algorithm , mathematics , artificial intelligence , machine learning , epistemology , mathematical analysis , philosophy , pure mathematics
Self‐modeling curve resolution (SMCR) techniques are widely applied for resolving chemical data to the pure‐component spectra and composition profiles. In most circumstances, there is a range of mathematical solutions to the curve resolution problem. The mathematical solutions generated by SMCR obey the applied constraints coming from a priori physicochemical information about the system under investigation. However, several studies demonstrate that a unique solution can be obtained by implementing some constraints such as trilinearity, equality, zero concentration region, correspondence, local‐rank, and non‐negativity under data‐based uniqueness (DBU) condition. In this research, a general rule for uniqueness (GRU) is proposed to unify all the different information that lead to a unique solution in one framework. Moreover, GRU can be a guide for developing new constraints in SMCR to get more accurate solutions. The authors are delighted to dedicate this manuscript to Professor Paul J. Gemperline in recognition of his significant contributions to the field of chemometrics. We believe that the chemometrics society's success in addressing its mission owes a great deal to his vision, passion for learning and teaching, and extensive scientific efforts over the years. We honor his friendship and generous supports.