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

Self Cite

A major problem of multivariate curve resolution methods is the underlying non-uniqueness of the pure component decompositions. This raises the question how a chemical experiment should be designed so that the solution ambiguity is as small as possible. Changes of the reaction conditions belong to the possible variations whereas for a fixed chemical reaction system, the pure component spectra appear to be unchangeable. The paper investigates and discusses the possibility to design a chemical experiment in a way that minimizes the ambiguity of the factorization. The analysis identifies regions of the spectra that are responsible for a small ambiguity. Certain sources are identified that are responsible for an increased ambiguity by means of an a posteriori analysis. This results in recommendations how to construct spectral measurements incorporating a reduced factorization ambiguity. Furthermore, lower bounds on an unavoidable base level of ambiguity are specified under the constraint of fixed reactants. The problem analysis is accompanied by investigations of several experimental data sets. KEYWORDS ambiguity, design of experiments, multivariate curve resolutionJournal of Chemometrics. 2020;34:e3159.wileyonlinelibrary.com/journal/cem

Section: Borgen Plots and Rotational Ambiguity In Afs Constructionsmentioning

confidence: 99%

“…In particular, for s =3, the 2‐simplices are triangles that enclose INNPOL and are included in Borgen and Kowalski and Rajkó and István . A simultaneous construction of

M_{S}

and

M_{C}

is possible by using certain duality relations between

I_{C}

and

F_{S}

and also

I_{S}

and

F_{C}

…”

Section: Borgen Plots and Rotational Ambiguity In Afs Constructionsmentioning

confidence: 99%

“…The resulting polyhedron is compared with the reference solution

F_{C}

. For s =3, the polyhedra are (planar) polygons and are computed by the polygon inflation procedure . Hence, the computations are stable even for noisy data.…”

Section: Borgen Plots and Rotational Ambiguity In Afs Constructionsmentioning

confidence: 99%

“…The AFS‐sets

M_{S}

and

M_{C}

Section: Application To Experimental Spectral Datamentioning

confidence: 99%

“…Data set 3. The polygons

F_{C}

and

F_{S}

Section: Application To Experimental Spectral Datamentioning

confidence: 99%

See 3 more Smart Citations

Multivariate curve resolution methods and the design of experiments

Sawall

Kubis

Schröder

et al. 2019

Self Cite

On the area of feasible solutions for rank‐deficient problems: I. Introduction of a generalized concept

Sawall

Neymeyr

2020

Self Cite

Rank deficiency of a spectral data matrix means that its rank is smaller than the number of the anticipated chemical components. A rank deficiency can hide the true chemical structure of the underlying pure components and complicates the application of multivariate curve resolution and self‐modeling curve resolution techniques. A new approach for the analysis of the factor ambiguities is introduced, and the area of feasible solutions (AFS) is generalized to rank‐deficient spectral data. The extended tools are tested for the Michaelis–Menten kinetics and abstract model data.

Two new methods for the estimation and interpretation of the range of feasible profiles in multivariate curve resolution and their implications to analytical chemistry

Olivieri

2024

Two new models have been recently introduced for studying the remaining rotational ambiguity in the bilinear decomposition of matrix data. One of the models is N‐BANDS, which yields two extreme profiles per sample component, corresponding to maximum or minimum signal contribution function or relative component area under its concentration profile. It is highly useful for computing the relative root mean square error due to rotational ambiguity in estimated analyte concentrations (RMSERA), which numerically quantifies the impact of the phenomenon in terms of prediction uncertainty. Since N‐BANDS successfully consider the presence of instrumental noise in the data, it is extremely useful for the analysis of real data sets. The other model is SW‐N‐BANDS, which is similar to N‐BANDS, but is applied in a sensor wise manner, that is, computing the maximum and minimum intensity value at each sensor. It provides the boundaries of the full set of feasible profiles, and helps to better understand the behavior of a given component under the application of several constraints. Both models are described in light of both simulations and experimental data, illustrating their main characteristics of importance to analytical chemistry studies.