Simultaneous construction of dual Borgen plots. II: Algorithmic enhancement for applications to noisy spectral data

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EarlyView Article

  • Published: Mar 8, 2018
  • Author: Mathias Sawall, Annekathrin Moog, Christoph Kubis, Henning Schröder, Detlef Selent, Robert Franke, Alexander Brächer, Armin Börner, Klaus Neymeyr

Abstract

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.

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