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Simultaneous construction of dual Borgen plots. II: Algorithmic enhancement for applications to noisy spectral data
Author(s) -
Sawall Mathias,
Moog Annekathrin,
Kubis Christoph,
Schröder Henning,
Selent Detlef,
Franke Robert,
Brächer Alexander,
Börner Armin,
Neymeyr Klaus
Publication year - 2018
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.3012
Subject(s) - mathematics , dual (grammatical number) , matrix (chemical analysis) , omega , physics , art , materials science , literature , quantum mechanics , composite material
Borgen plots are low‐dimensional representations of the set of all nonnegative factorizations of spectral data matrices. Classical Borgen plots are limited to nonnegative data and can be constructed for the spectral factor or for the concentration profiles. In the first part of this paper, a simultaneous construction of the two dual Borgen plots is presented, which intensively exploits the underlying duality principles. The second part introduces algorithmic enhancements which make the simultaneous Borgen plot construction possible for noisy experimental data matrices which can contain small negative matrix entries. The new method is tested for FT‐IR spectral data from the Rhodium catalyzed hydroformylation process. The results are compared to those by the FACPACK ‐implementation of the polygon inflation method.