Extent Of Rotational Ambiguity Research Articles

Interference-free calibration with first-order instrumental data and multivariate curve resolution. When and why?

The possibility of building an interference-free calibration with first-order instrumental data with multivariate curve resolution-alternating least-squares (MCR-ALS) has been a recent topic of interest. When the protocols were successful, MCR-ALS proved to be suitable for the extraction of chemically meaningful information from first-order calibration datasets, even in the presence of unexpected species, i.e., constituents present in the test samples but absent in the calibration set. This may represent an interesting advantage over classical first-order models, e.g. partial least-squares regression (PLS). However, the predictive capacity of MCR-ALS models can be severely affected by rotational ambiguity (RA), which is usually present in first-order datasets when interferents occur, and has not been always characterized in the published analytical protocols. The aim of this report is to discuss important issues regarding MCR-ALS modelling of first-order data for a calibration scenario with a single analyte and one interferent through simulated and experimental data. Specifically, the question of when and why MCR-ALS allows one to build interference-free calibration models with first-order data is studied in terms of signal overlapping, extent of RA, and especially the role of ALS initialization procedures in prediction performance. The aim is to alert analytical chemists that interference-free MCR-ALS with first-order data may not always be successful.

A conceptual view to the area correlation constraint in multivariate curve resolution

Multivariate curve resolution (MCR) techniques are widely employed to study chemical systems and unravel underlying physic-chemical information. Different constraints have been introduced to reduce the extent of uncertainty in the results of MCR-ALS. It is important to study the effect of each constraint on the range of feasible solutions in the curve-resolution studies. As each constraint uses specific information, constraints have different effects on the amount of uncertainty.In the present contribution, condition which resulted in uniqueness applying area correlation constraint (ACC) was illustrated. Additionally, the effect of area correlation constraint (relative known-value constraints) on the amount of uncertainty in the resolved profiles was investigated and visualized in detail. Besides, some rules were established for determining the required number and composition of calibration samples. To illustrate how ACC leads to the uniqueness of a MCR result in the presence of validation samples, the extent of rotational ambiguity was evaluated by analyzing different simulated and experimental data sets. The latter involves the quantification of Phenylalanine and Tyrosine in a second-order excitation-emission fluorescence data sets.

Closure constraint in multivariate curve resolution

AbstractMultivariate curve resolution techniques try to estimate physically and/or chemically meaningful profiles underlying a set of chemical or related measurements. However, the estimation of profiles is not generally unique and it is often complicated by intensity and rotational ambiguities. Constraints as further information of chemical entities can be imposed to reduce the extent of ambiguities. Not only a long list of constraints has been introduced but also some of them can be applied in different ways. Either investigating constraint effects on the extent of rotational ambiguity or how they can be applied during curve resolution can shed light on curve resolution studies. The motivation behind this contribution is to pave the way to a clarification about the closure constraint. Considering simulated equilibrium and kinetic spectrophotometric data sets, different approaches to closure implementation were applied to demonstrate the geometrical explanation of closure constraint and its effect on multivariate curve resolution‐alternating least squares results. Besides, the closure constraint is compared with normalization and it is proved that the closure constraint is a Borgen norm and has the same effect as other Borgen norms in multivariate curve resolution. Finally, to further examine the closure constraint, a real data set was investigated.

Effect of adding variables on rotational ambiguity in positive matrix factorization solutions

A major problem that limit the use of the model-free analysis methods, like positive matrix factorization (PMF), for the resolution of multivariate data is that usually, there is rotational ambiguity in the results. Implementing adequate constraints may reduce such ambiguities. In some special cases, non-negativity constraints may serve as a sufficient condition to uniquely resolve profiles. In this study, effect of adding new variables on the extent of rotational ambiguity is investigated, and profiles with lower rotation have been obtained on the basis of data set structure. The displacement (DISP) method of error estimation (EE) for the factor elements incorporated into the US Environmental Protection Agency's version of positive matrix factorization (PMF) has been applied to capture the uncertainty of PMF analyses due to rotational ambiguity. To explore these considerations, results are presented for synthetic including submicron particle size distributions (12–470nm) measured between January 2008 and December 2010 at the New York State Department of Environmental Conservation (NYS DEC) site in Rochester, NY. Generally, added informative variables can reduce the ambiguity in the profiles. The results of the PMF analysis showed the effect of adding new variables to feasible solutions led to significantly decreased (up to 44%) DISP intervals. More robust results with lower rotational uncertainty became possible and the results were more easily interpreted. This approach can be applied to any other field that utilize quantitative factor analysis methods.

Resolving of challenging gas chromatography–mass spectrometry peak clusters in fragrance samples using multicomponent factorization approaches based on polygon inflation algorithm

Analysis of fragrance composition is very important for both the fragrance producers and consumers. Unraveling of fragrance formulation is necessary for quality control, competitor and trace analysis. Gas chromatography–mass spectrometry (GC–MS) has been introduced as the most appropriate analytical technique for this type of analysis, which is based on Kovats index and MS database. The most straightforward method to analyze a GC–MS dataset is to integrate those peaks that can be recognized by their mass profiles. But, because of common problems of chromatographic data such as spectral background, baseline offset and specially overlapped peaks, accurate quantitative and qualitative analysis could be failed. Some chemometric modeling techniques such as bilinear multivariate curve resolution (MCR) methods have been introduced to overcome these problems and obtained well resolved chromatographic profiles. The main drawback of these methods is rotational ambiguity or nonunique solution that is represented as area of feasible solutions (AFS).Polygonal inflation algorithm (PIA) is an automatic and simple to use algorithm for numerical computation of AFS. In this study, the extent of rotational ambiguity in curve resolution methods is calculated by MCR-BAND toolbox and the PIA. The ability of the PIA in resolving GC–MS data sets is evaluated by simulated GC–MS data in comparison with other popular curve resolution methods such as multivariate curve resolution alternative least square (MCR-ALS), multivariate curve resolution objective function minimization (MCR-FMIN) by different initial estimation methods and independent component analysis (ICA). In addition, two typical challenging area of total ion chromatogram (TIC) of commercial fragrances with overlapped peaks were analyzed by the PIA to investigate the possibility of peak deconvolution analysis.