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On generalized Borgen plots II: The line‐moving algorithm and its numerical implementation
Author(s) -
Jürß Annekathrin,
Sawall Mathias,
Neymeyr Klaus
Publication year - 2016
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.2815
Subject(s) - mathematics , computation , construct (python library) , set (abstract data type) , algorithm , line (geometry) , computer science , geometry , programming language
Borgen plots are geometric constructions that represent the set of all nonnegative factorizations of spectral data matrices for three‐component systems. The classical construction by Borgen and Kowalski (Anal. Chim. Acta 174, 1‐26 (1985)) is limited to nonnegative data and results in nonnegative factorizations. The new approach of generalized Borgen plots allows factors with small negative entries. This makes it possible to construct Borgen plots for perturbed or noisy spectral data and stabilizes the computation. In the first part of this paper, the mathematical theory of generalized Borgen plots has been introduced. This second part presents the line‐moving algorithm for the construction of generalized Borgen plots. The algorithm is justified, and the implementation in the FACPACK software is validated.