Investigation of the equality constraint effect on the reduction of the rotational ambiguity in three-component system using a novel grid search method

Enhancing gas chromatography-mass spectrometry resolution and pure analyte discovery using intra-chromatogram elution profile matching

Chemometric decomposition methods like multivariate curve resolution-alternating least squares (MCR-ALS) are often employed in gas chromatography-mass spectrometry (GC-MS) to improve analyte identification and quantitation. However, these methods can perform poorly for analytes with a low chromatographic resolution (Rs) and a high degree of spectral contamination from noise and background interferences. Thus, we propose a novel computational algorithm, termed mzCompare, to improve analyte identification and quantitation when coupled to MCR-ALS. The mzCompare method utilizes an underlying requirement that the retention time and peak shape between mass channels (m/z) of the same analyte should be similar. By discovering the selective m/z for a given analyte in a chromatogram, a pure elution profile can be generated and used as an equality constraint in MCR-ALS. The performance of the mzCompare methodology is demonstrated with both experimental and simulated chromatograms. Experimentally, unresolved analytes with a Rs as low as 0.05 could be confidently identified with mzCompare assisted MCR-ALS. Furthermore, application of the mzCompare algorithm to a complex aerospace fuel resulted in the discovery of 335 analytes, a 44 % increase compared to conventional peak detection methods. GC-MS simulations of target-interferent analyte pairs demonstrated that the performance of MCR-ALS deteriorated below a Rs of ∼0.25. However, mzCompare assisted MCR-ALS showed excellent identification and acceptable quantitative accuracy at a Rs of ∼0.02. These results show that the mzCompare algorithm can help analysts overcome modeling ambiguities resulting from the chemometric multiplex disadvantage.

A multi-method chemometric analysis in spectroelectrochemistry: Case study on molybdenum mono-dithiolene complexes

Spectroelectrochemical (SEC) analyses combine spectroscopic measurements with electrochemical techniques and can provide deep insight into complex multi-component chemical reaction systems. SEC experiments typically produce large amounts of spectroscopic data. Chemometric techniques are required for the data analysis and aim at extracting the underlying pure component information. Here we analyze spectroelectrochemically gained UV-vis data from five molybdenum mono-dithiolene complexes with changing redox states. SEC enables an electrochemical control of the mixture composition which supports the application of chemometric curve resolution techniques. The factor ambiguity problem is addressed by a multi-method approach combining chemometric tools from the evolving factor analysis (EFA) and from the area of feasible solutions (AFS) methodology in combination with factor duality arguments. EFA enables a subsystem analysis. Two subsystems with three species each are identified, which belong to a reductive and to an oxidative region. A joint species is contained in both regions. A complete pure component decomposition becomes possible in a final step.

Workflow for the Supervised Learning of Chemical Data: Efficient Data Reduction-Multivariate Curve Resolution (EDR-MCR)

A new method termed efficient data reduction-multivariate curve resolution (EDR-MCR) has been devised for classification of high-dimensional data. The method introduces the coupling of EDR and MCR as a new strategy for data splitting, variable selection, and supervised classification of high dimensionality data. The method reduces data dimensionality and selects the training set using principal component analysis (PCA) and convex geometry prior to data classification. Then, the reduced data are categorized using an MCR model, in which numerical constraints are imposed to resolve the data into classes and readily interpretable pure component signal weights. The performance of the EDR and supervised MCR methods were tested for their ability to enable discrimination between the constituents of two benchmark and two high-dimensional data sets. The results were compared with the output of the application of different data splitting methods including iterative random selection (IRS), Kennard-Stone (KS), and discrimination methods including partial least-squares-discriminant analysis (PLS-DA) and the ensemble-learning frameworks of linear discriminant analysis (LDA), k-nearest neighbors (KNN), classification and regression trees (CART), and support vector machine (SVM). Overall, EDR resulted in comparable results with other data splitting methods despite the small size of the training set samples that it created. The proposed MCR approach, in comparison with other commonly used supervised techniques, has the advantages of speed in implementation, tuning of fewer parameters, flexibility in the analysis of data characterized by low sample numbers and class imbalances, improved accuracy from the inclusion of additional system information in the form of numerical constraints, and the ability to resolve pure components signal weights.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e., when selected analytes are determined in unknown samples having unexpected constituents, not considered in the calibration set of samples. It is therefore imperative that analytical chemists developing second-order multivariate calibration methods using MCR-ALS acknowledge the relevance of this issue, and more importantly, have access to the required tools to size the relative impact of this potential source of uncertainty on the estimated analyte concentrations. The purpose of this tutorial is to provide a down-to-earth view of rotational ambiguity, by studying in detail a synthetic example mimicking a typical chromatographic-spectral experiment, where a set of calibration samples is joined with an unknown sample having an uncalibrated interference. After explaining the background information needed to understand the origin of the phenomenon, the available tools for the estimation of the feasible MCR-ALS solutions and the derived uncertainty on analyte predictions will be discussed. A multi-component experimental system will also be discussed, stressing the fact that rotational ambiguity uncertainties, however small, should always be estimated and reported.

Soft-trilinear constraints for improved quantitation in multivariate curve resolution

Soft trilinearity constraints give a range of feasible solutions (grey) that envelop the true solution (blue). PARAFAC2 (green) and MCR-ALS results (black) are shown for comparison.

Enhanced target factor analysis

Target testing or target factor analysis, TFA, is a well-established soft analysis method. TFA answers the question whether an independent target test vector measured at the same wavelengths as the collection of spectra in a data matrix can be excluded as the spectrum of one of the components in the system under investigation. Essentially, TFA cannot positively prove that a particular test spectrum is the true spectrum of one of the components, it can, only reject a spectrum. However, TFA will not reject, or in other words TFA will accept, many spectra which cannot be component spectra. Enhanced Target Factor Analysis, ETFA addresses the above problem. Compared with traditional TFA, ETFA results in a significantly narrower range of positive results, i.e. the chance of a false positive test result is dramatically reduced. ETFA is based on feasibility testing as described in Refs. [16-19]. The method has been tested and validated with computer generated and real data sets.