Parallel Factor Analysis 2 Research Articles

Probabilistic PARAFAC2.

The Parallel Factor Analysis 2 (PARAFAC2) is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example, because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable to improve robustness to noise and provide a principled approach for determining the number of factors, but challenging because direct model fitting requires that factor loadings be decomposed into a shared matrix specifying how the components are consistently co-expressed across samples and sample-specific orthogonality-constrained component profiles. We develop two probabilistic formulations of the PARAFAC2 model along with variational Bayesian procedures for inference: In the first approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the second, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulations to the conventional direct fitting algorithm based on maximum likelihood on synthetic data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data showing that the probabilistic formulations are more robust to noise and model order misspecification. The probabilistic PARAFAC2, thus, forms a promising framework for modeling multi-way data accounting for uncertainty.

A novel and intelligent molecularly imprinted enzymatic biosensor for biosensing of human serum albumin in the presence of gamma-globulin, and glucose as uncalibrated interference

Human serum albumin (HSA) is not electroactive, because the electroactive amino acids have been buried in its structure. Therefore, direct electrochemical determination of the HSA as the most abundant protein in human plasma cannot be performed. In this work, a novel electrochemical biosensor has been developed based on synthesis of dual templates molecularly imprinted polymers (DTMIPs) having trypsin (TRP) and HSA as template molecules onto the surface of a glassy carbon electrode (GCE) modified with graphene-ionic liquid (Gr-IL). By incubation of the biosensor with TRP, and HSA, tryptic hydrolysis of the HSA is occurred which breaks the HSA down into free amino acids. The HSA involves five electroactive amino acids including cysteine, tryptophan, tyrosine, methionine and histidine whose differential normal pulse voltammetric (DNPV) responses are overlapped and generated a single peak. In order to increase the sensitivity of the DTMIP/Gr-IL/GCE for determination of the HSA, hydrodynamic DNPV (HDNPV) data were generated, and used for analytical purposes. The second-order HDNPV data were generated at different pulse amplitudes and used to develop four second-order calibration models by multivariate curve resolution-alternating least squares (MCR-ALS), parallel factor analysis2 (PARAFAC2), multi-way partial least squares/residual bilinearization (N-PLS/RBL), and unfolded partial least squares/residual bilinearization (U-PLS/RBL) to select the best procedure for determination of the HSA in the presence of gamma-globulin and glucose as uncalibrated interferences. The results confirmed the best performance for the biosensor assisted by MCR-ALS for ultrasensitive and selective determination of the HSA in both synthetic and real matrices which was comparable with HPLC-UV as a reference method.

Monitoring pollution pathways in river water by predictive path modelling using untargeted GC-MS measurements

To safeguard the quality of river water, a comprehensive approach is required within the European Water Framework Directive. It is vital to conduct non-target screening of the complete chemical fingerprint of the aquatic ecosystem, as this will help to identify chemicals of emerging concern and uncover their unusual dynamic patterns in river water. Achieving this goal calls for an advanced combination of two measurement paradigms: tracing the potential pollution path through the river network and detecting the numerous compounds that constitute the chemical composition, both known and unknown. To address this challenge, we propose an integrated approach that combines the preprocessing of ongoing Gas Chromatography Mass Spectrometry (GC-MS) measurements at nine sites along the Rhine using PARAllel FActor Analysis2 (PARAFAC2) for non-target screening, with spatiotemporal modelling of these sites within the river network using a statistical path modelling algorithm called Process Partial Least Squares (Process PLS). With an average explained variance of 97.0%, PARAFAC2 extracted mass spectra, elution, and concentration profiles of known and unknown chemicals. On average, 76.8% of the chemical variability captured by the PARAFAC2 concentration profiles was extracted by Process PLS. The integrated approach enabled us to track chemicals through the Rhine catchment, and tentatively identify known and as-yet unknown potential pollutants, including methyl tert-butyl ether and 1,3-cyclopentadiene, based on non-target screening and spatiotemporal behaviour.

An upgrade of MVC2, a MATLAB graphical user interface for second-order multivariate calibration: Beyond trilinear models

In the present report, an upgrade of a MATLAB graphical user interface (GUI) toolbox for implementing second-order multivariate calibration models is presented, named Multivariate Calibration 2 (MVC2). Due to the advances in the chemometric field, this software has undergone numerous changes since its last release in 2009. The new freely available MVC2 incorporates novel features and models that make it a very practical tool for data processing. Overall, the current version presents different types of algorithms, designed to provide specific degrees of model flexibility for different multi-way data scenarios: in addition to trilinear decomposition (TLD) and residual bilinearization (RBL) models, which were previously included in the 2009 version, parallel factor analysis 2 (PARAFAC2) and multivariate curve resolution (MCR) methods are now available. All these chemometric methodologies are integrated in the software for quantitative purposes, and if needed, they permit to exploit the so-called analytical second-order advantage. The program offers practical tools for data loading and visualization, model development and validation, and prediction in unknown samples. The software output also includes a comprehensive report on the analytical figures of merit (AFOMs) applicable to second-order calibration models. Specifically, a tool was incorporated for the diagnosis of the remaining rotational ambiguity in the MCR solutions. In the present report, the new features of MVC2 are illustrated through simulated examples and real calibration datasets.

PARAFAC2×N: Coupled decomposition of multi-modal data with drift in N modes.

Analysis of GC×GC-TOFMS data for large numbers of poorly-resolved peaks, and for large numbers of samples remains an enduring problem that hinders the widespread application of the technique. For multiple samples, GC×GC-TOFMS data for specific chromatographic regions manifests as a 4th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel is for all practical purposes nonexistent. A number of solutions to handling GC×GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection. The proposed model captures over 99.9% of variance for a synthetic data set, presenting an extreme example of peak drift and co-elution across two modes of separation.

An intelligent biosensing procedure based on three-way calibrations and generation of second-order hydrodynamic square wave voltammetric data for detection of DNA damage and simultaneous biosensing of three polycyclic aromatic hydrocarbons

In this work, we have generated second-order hydrodynamic square wave voltammetric (HSWV) data and analyzed them by multivariate curve resolution-alternating least squares (MCR-ALS) for simultaneous determination of the rates of deoxyribonucleic acid (DNA) damages induced by benzo(a)pyrene (BP), dibenzo(a,e)pyrene (DBP) and indeno(1,2,3-cd)pyrene (IP). A thick-film boron doped diamond electrode (TFBDDE) was used as the platform of the biosensor, and it was modified by graphene (GR), cobalt nanoparticles (Co NPs), horseradish peroxidase (HRP), and DNA. The double stranded DNA and HRP were immobilized onto the surface of Co NPs/GR/TFBDDE by the use of nafion. The HRP in the presence of hydrogen peroxide (H2O2) can mimic enzymatic effects of cytochrome P450 (CP450) to metabolize BP, DBP, and IP to cause DNA damage. The HSWV responses of DNA-HRP/Co NPs/GR/TFBDDE to BP, DBP, and IP were individually calibrated to obtain individual rates of DNA damages induced by BP, DBP, and IP. Then, the second-order HSWV data were generated and modeled by parallel factor analysis2 (PARAFAC2), MCR-ALS, multi-way partial least squares/residual bilinearization (N-PLS/RBL), and unfolded partial least squares/residual bilinearization (U-PLS/RBL) to choose the best second-order calibration model for simultaneous determination of rates of DNA damages induced by BP, DBP and IP. The biosensor assisted by MCR-ALS showed the best performance among the mentioned algorithms, and it was expanded to simultaneous determination of BP, DBP and IP whose performance was compared by the biosensor assisted by amperometric data as well. Interestingly, the biosensor assisted by amperometric data and RBF-PLS showed a better performance in simultaneous determination of BP, DBP and IP. The biosensor assisted by amperometric data and RBF-PLS was successful in simultaneous determination of BP, DBP and IP in wastewater samples as real matrices. Protective effects of the Myrtus communis L extract against DNA damage was also investigated, and our records confirmed antioxidant effects of Myrtus communis L extract against DNA damage.

Sensitive and selective simultaneous biosensing of nandrolone and testosterone as two anabolic steroids by a novel biosensor assisted by second-order calibration

Recently, our research group have focused on an interesting project in which a novel dual template molecularly imprinted (DTMIP) biosensor was fabricated and assisted by second-order differential pulse voltammetric (DPV) data for simultaneous determination of nandrolone decanoate (ND) and testosterone decanoate (TS). An indium tin oxide (ITO) was modified with multiwalled carbon nanotubes-graphene-ionic liquid (MWCNT-Gr-IL) and then, the fullerene C60 was casted onto the surface of MWCNT-Gr-IL/ITO and electrochemically reduced. Finally, DTMIPs were electrosynthesized by electropolymerization of 4-aminobenzoic acid (ABA) as monomer with ND and TS as template molecules to obtain the final structure of the biosensor (DTMIP/C60/MWCNT-Gr-IL/ITO). Structure of the biosensor was electrochemically and microscopically characterized. The ND and TS generated two severely overlapped DPVs at the surface of the biosensor which forced us to assist the biosensor with three-way calibration by second-order DPV data to simultaneous determine them. Two second-order algorithms including multivariate curve resolution alternating least squares (MCR-ALS) and parallel factor analysis2 (PARAFAC2) were used to build second-order calibration models and evaluation of their performance in the analysis of synthetic samples showed more superiority of the MCR-ALS than PARAFC2 which motivated us to select PARAFC2 for the analysis of urine samples as real cases. Application of the biosensor assisted by PARAFC2 for the analysis of urine samples towards simultaneous determination of ND and TS was successful.

A new multi-factor multi-objective strategy based on a factorial presence-absence design to determine polymer additive residues by means of head space-solid phase microextraction-gas chromatography-mass spectrometry

A new multi-factor multi-objective strategy to approach the joint assessment of the effect of six experimental factors in the determination by head space-solid phase microextraction-gas chromatography-mass spectrometry (HS-SPME-GC-MS) of eight different additives commonly used in the plastic packaging manufacturing is proposed in this work. Five HS-SPME experimental factors, both qualitative and quantitative, are explored: the type of fiber, addition of salt, extraction and desorption time, and extraction temperature. The effect of these factors is studied through a factorial presence-absence model, that include interactions, using a D-optimal design. As a result, the number of experiments is reduced from 128, full factorial design, to 14. The effect of carrying out the measurements in different experimental sessions is considered by including a blocking factor. The response for each compound is estimated in the experimental domain and then the best experimental conditions are chosen by using Pareto front. Parallel coordinates are employed to show the conflicting conditions intrinsic to a multi-objective analysis when compounds of different nature are extracted by HS-SPME. Parallel factor analysis 2 (PARAFAC2) decomposition is used because it makes the determination of target compounds in the presence of unknown interferents possible, which enables the unequivocal identification of target compounds according to official regulations. The developed method is applied to determine 2,6-di-tert-butyl-4-methyl-phenol (BHT), benzophenone (BP), bis(2-ethylhexyl) adipate (DEHA), diethyl phthalate (DEP), diisobutyl phthalate (DiBP), dibutyl phthalate (DBP), benzyl butyl phthalate (BBP) and bis(2-ethylhexyl) phthalate (DEHP). The level of these compounds found in nine types of bottled natural still and sparkling mineral waters is very low, so the compounds were not present in quantities that may be injurious to human health.

Obtaining clean and informative mass spectra from complex chromatographic and high-resolution all-ions-fragmentation data by nonnegative parallel factor analysis 2

A major challenge in processing of complex data obtained from chromatography hyphenated to mass spectrometry is to resolve chromatographically co-eluting compounds. In this study, we present a workflow for the resolution of ultra-high pressure liquid chromatography high-resolution mass spectrometry data obtained by the broadband data-independent acquisition MSE operation (UHPLCHRMSE). The workflow is based on a recently introduced algorithm for Parallel Factor Analysis 2 (PARAFAC2) that allows to enforce non-negativity on all the model coefficients. The workflow was tested on three sets of UHPLC-HRMSE measurements from a Lupinus angustifolius L. crop field study, which included plant tissue samples, soil samples and samples from drainage water as well as stream water close to the field. The three datasets included 93, 59, and 75 chromatographic runs in total for the plant, soil and water batches, respectively.Nonnegative-PARAFAC2 models were fitted on the summed high and low energy (HE and LE) traces on chromatographic intervals corresponding to spiked standard for the three sample sets independently. In soil and plant samples, 13 out of 14 spiked standards were resolved by NN-PARAFAC2 even in presence of chromatographic co-elution, and their mass spectral loadings could be matched to a reference spectrum. In contrast, only seven spiked standards were correctly resolved and matched for the water samples because a higher chromatographic baseline rendered the data noisier.The results show that the workflow we present can provide improved mass spectral selectivity for data-independent acquisition compared to using the raw mass spectra and can be used to match fragment ions from the HE trace, and precursor and adduct ions from the LE trace even in presence of co-eluting compounds.

Cross-lingual transfer learning: A PARAFAC2 approach

The proposed framework addresses the problem of cross-lingual transfer learning resorting to Parallel Factor Analysis 2 (PARAFAC2). To avoid the need for multilingual parallel corpora , a pairwise setting is adopted where a PARAFAC2 model is fitted to documents written in English (source language) and a different target language. Firstly, an unsupervised PARAFAC2 model is fitted to parallel unlabelled corpora pairs to learn the latent relationship between the source and target language. The fitted model is used to create embeddings for a text classification task (document classification or authorship attribution). Subsequently, a logistic regression classifier is fitted to the training source language embeddings and tested on the training target language embeddings. Following the zero-shot setting, no labels are exploited for the target language documents. The proposed framework incorporates a self-learning process by utilizing the predicted labels as pseudo-labels to train a new, pseudo-supervised PARAFAC2 model, which aims to extract latent class-specific information while fusing language-specific information. Thorough evaluation is conducted on cross-lingual document classification and cross-lingual authorship attribution . Remarkably, the proposed framework achieves competitive results when compared to deep learning methods in cross-lingual transfer learning tasks.

Simultaneous Determination of Adulterants in Dietary Food Supplements Using Multivariate Data Analysis after Preconcentration with Novel Nanosorbents and Chromatographic Measurement.

The increasing popularity of dietary supplements and, consequently, related adulteration emphasizes the rising need to examine the association of food supplements with fraud. Intentional or unintentional fraud in food supplements by hazardous chemicals compounds is a problem that many countries are struggling with. Much effort have been made to effectively and reliably control the quality of food supplements. Due to the importance of the subject, an analytical method for the simultaneous and reliable detection and quantitative determination of three key adulterants in dietary food supplements was developed. The proposed method benefits from analytical methods and multivariate calibration methods to progress the determination of adulterants in a complex matrix. HPLC assisted by multivariate curve resolution-alternating least square (MCR-ALS) analysis was used to detect adulterants in real samples after separation and preconcentration using novel mesoporous carbon nanoparticles. Solid-phase extraction (SPE) optimization was accomplished by central composite design (CCD). In order to obtain the best results, the MCR-ALS model was compared with the parallel factor analysis 2 (PARAFAC2) model and validated by estimation of linearity, detection limits, and recovery. The detection limits and linear dynamics were calculated as 1.5, 4.27, and 4.77 µg/mL, and 1-50, 5-20, and 5-20 µg/mL for caffeine, ephedrine, and fluoxetine, respectively. Mean recovery for determination of caffeine, ephedrine, and fluoxetine using the developed method was reported as 101.75, 91.7, and 92.36, respectively. The results showed that to avoid negative health outcomes associated with the excessive consumption of adulterated food supplements releasing such products should be carefully regulated. The developed method was validated using statistical factors and showed acceptable and reliable results. (1) The application of MCR-ALS coupled with HPLC-Diode-Array Detection data sets allowed the simultaneous identification and quantification of three key adulterants (caffeine, ephedrine, and fluoxetine) in dietary food supplements. (2) A small amount of the novel adsorbent was successfully used to preconcentrate the trace amounts of adulterants in samples. (3) This method benefits from the chemometrics tools and experimental design to significantly reduce the use of toxic solvents and complicated instruments to propose a less time-consuming method for quantification of multicomponents in the presence of uncalibrated interferents.

Automatic and non-targeted analysis of the volatile profile of natural and alkalized cocoa powders using SBSE-GC-MS and chemometrics

A total of 56 key volatile compounds present in natural and alkalized cocoa powders have been rapidly evaluated using a non-target approach using stir bar sorptive extraction gas chromatography mass spectrometry (SBSE-GC–MS) coupled to Parallel Factor Analysis 2 (PARAFAC2) automated in PARADISe. Principal component analysis (PCA) explained 80% of the variability of the concentration, in four PCs, which revealed specific groups of volatile characteristics. Partial least squares discriminant analysis (PLS-DA) helped to identify volatile compounds that were correlated to the different degrees of alkalization. Dynamics between compounds such as the acetophenone increasing and toluene and furfural decreasing in medium and strongly alkalized cocoas allowed its differentiation from natural cocoa samples. Thus, the proposed comprehensive analysis is a useful tool for understanding volatiles, e.g., for the quality control of cocoa powders with significant time and costs savings.

Interpretation of matrix chromatographic-spectral data modeling with parallel factor analysis 2 and multivariate curve resolution

Parallel factor analysis 2 (PARAFAC2) is still being advocated for the processing of second-order chromatographic-spectral data, both for qualitative and quantitative applications. However, neither classical PARAFAC2 nor the newly developed flexible non-negative NN-PARAFAC2 version can adequately model these data in a general situation. In quantitative analysis, considerable bias may result in the estimation of analyte concentrations, due to the fact that both PARAFAC2 models apply an artificial constraint to the retrieved profiles, requiring constant cross-product, i.e., constant overlapping, between all pairs of component elution profiles in all samples. This only occurs under limited conditions. In this report, simulations help to understand, visualize and interpret these PARAFAC2 features. Experimental data are also studied concerning the determination of a fluoroquinolone antibiotic in bovine liver samples by liquid chromatography with multi-wavelength fluorescence detection. Both for simulated and experimental data, the PARAFAC2 versions provide poor analytical results, while correct data processing and reasonable analytical indicators can be achieved using multivariate curve resolution - alternating least-squares (MCR-ALS). For the simulated data sets, root mean square errors/relative errors of prediction were 0.01 concentration units/2% for MCR-ALS, compared to 0.02–0.06 units/4–12% for both PARAFAC2 and NN-PARAFAC2. For the experimental data sets, they were 0.025 µg mL−1/11% for MCR-ALS, 0.09 µg mL−1/40% for PARAFAC2 and 0.16 µg mL−1/71% for NN-PARAFAC2, with average recoveries (standard deviation) of 91(14)%, 185(135)% and 69(35)% respectively.

Using deep learning to evaluate peaks in chromatographic data

Analysis of untargeted gas-chromatographic data is time consuming. With the earlier introduction of the PARAFAC2 (PARAllel FACtor analysis 2) based PARADISe (PARAFAC2 based Deconvolution and Identification System) approach in 2017, this task was made considerably more time-efficient. However, there are still a number of manual steps in the analysis which require data analytical expertise. One of these is the need to define whether or not each PARAFAC2 resolved component represents a peak suitable for integration. As the peaks may change in both shape and location on the elution time-axis, this presents a problem which cannot be readily solved by applying a linear classifier, such as PLS-DA (Partial Least Squares regression for Discriminant Analysis).As part of our ongoing efforts to further automate analysis of Gas Chromatography with Mass Spectrometry (GC-MS), we therefore explore a convolutional neural network classifier, capable of handling these shifts and variations in shape. The theory of convolutional neural networks and application on vector samples is briefly explained, and the performance is tested against a PLS-DA classifier, a shallow artificial neural network and a locally weighted regression model.The models are built on a training set with PARAFAC2 resolved components from eight different aroma related GC-MS runs with a total of over 70,000 elution profile samples, and validated using another, independent, GC-MS dataset.Based on Receiver Operating Characteristic curves (ROC) and manual analysis of the misclassified cases, it is shown that the convolutional network consistently outperforms the competing models, yielding an Area Under the Curve (AUC) value of 0.95 for peak classification. Examples are given illustrating that this new approach provides convincing means to automatically assess and evaluate modelled elution profiles of chromatographic data and thereby remove this laborious manual step.

Exploiting second-order advantage from mathematically modeled voltammetric data for simultaneous determination of multiple antiparkinson agents in the presence of uncalibrated interference

Abstract In this work, we are going to develop an efficient electroanalytical methodology based on generation of second-order differential pulse voltammetric (DPV) data at different pulse heights to exploit second-order advantage for simultaneous determination of levodopa (LDP), carbidopa (CDP), methyldopa (MDP), benserazide (BA), tolcapone (TOL) and entacapone (ENT) in the presence of dopamine (DPA) as uncalibrated interference. The recorded data were baseline- and potential shift-corrected by asymmetric least square spline regression (AsLSSR) and correlation optimized warping (COW) algorithms, respectively. After data pre-processing, multivariate curve resolution-alternating least squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2) were used to develop three-way calibration models and then, the abilities of the developed models to predict analytes’ concentrations in the absence and presence of DPA were examined in validation and test sets, respectively. MCR-ALS acted better than PARAFAC2 to predict analytes’ concentrations in the absence and presence of DPA as uncalibrated interference. Therefore, MCR-ALS was chosen to predict antiparkinson agents’ concentrations in spiked human serum samples as real cases. Fortunately, acceptable results were obtained which were comparable to those obtained by high performance liquid chromatography with UV detection (HPLC-UV) as reference method.

Application of Py-GC/MS coupled with PARAFAC2 and PLS-DA to study fast pyrolysis of genetically engineered poplars

Field-grown genetically engineered and wild-type poplars were pyrolyzed in a micro-pyrolysis (Py-GC/MS) setup under fast pyrolysis conditions. Poplars (Populus tremula x P. alba) down-regulated for cinnamoyl-CoA reductase (CCR), which catalyzes the first step of the monolignol-specific branch of the phenylpropanoid biosynthetic pathway, were grown in field trials in France and harvested after a full rotation of 2 years. The effect of small compositional differences, specifically small shifts in lignin composition and their impact on the bio-oil composition, could not be identified using principal component analysis (PCA), necessitating the use of more advanced analysis techniques. The combination of parallel factor analysis 2 (PARAFAC2) and partial least squares-discriminant analysis (PLS-DA) for detailed characterization and classification of the pyrolysis data enabled the classification of the poplars with a success rate above 99% using the PARAFAC2 scores. This methodology proved to be extremely valuable to identify subtle information in complex datasets, such as the one used in this study. The obtained PLS-DA models were validated by cross-validation, jackknifing and permutation tests in order to ensure that the model was not overfitting the data. PLS-DA showed that down-regulation of CCR disfavored the relative amount of both guaiacyl and syringyl lignin-derived compounds. This study shows that lignin engineering can be a promising strategy to alter the lignin composition of the biomass for the production of high value-added phenolic compounds.

Age interval and gender prediction using PARAFAC2 and SVMs based on visual and aural features

Parallel factor analysis 2 (PARAFAC2) is employed to reduce the dimensions of visual and aural features and provide ranking vectors. Subsequently, score level fusion is performed by applying a support vector machine (SVM) classifier to the ranking vectors derived by PARAFAC2 to make gender and age interval predictions. The aforementioned procedure is applied to the Trinity College Dublin Speaker Ageing database, which is supplemented with face images of the speakers and two single-modality benchmark datasets. Experimental results demonstrate the advantage of using combined aural and visual features for both prediction tasks.

Generation of non-multilinear three-way voltammetric arrays by an electrochemically oxidized glassy carbon electrode as an efficient electronic device to achieving second-order advantage: Challenges, and tailored applications

For the first time, several second-order calibration models based on artificial neural network-residual bilinearization (ANN-RBL), unfolded-partial least squares-RBL (U-PLS/RBL), multidimensional-partial least squares-RBL (N-PLS/RBL), multivariate curve resolution-alternating least squares (MCR-ALS), and parallel factor analysis 2 (PARAFAC2) were used to exploiting second-order advantage to identify which technique offers the best predictions for the simultaneous quantification of norepinephrine (NE), paracetamol (AC), and uric acid (UA) in the presence of pteroylglutamic acid (FA) as an uncalibrated interference at an electrochemically oxidized glassy carbon electrode (OGCE). Three-way differential pulse voltammetric (DPV) arrays were obtained by recording the DPV signals at different pulse heights. The recorded three-way arrays were both non-bilinear and non-trilinear therefore, the observed shifts in the recorded DPV data were corrected using correlation optimised warping (COW) algorithm. All the algorithms achieved the second-order advantage and were in principle able to overcome the problem of the presence of unexpected interference. Comparison of the performance of the applied second-order chemometric algorithms confirmed the more superiority of U-PLS/RBL to resolve complex systems. The results of applying U-PLS/RBL for the simultaneous quantification of the studied analytes in human serum samples were also encouraging.

Chemometric processing of second-order liquid chromatographic data with UV–vis and fluorescence detection. A comparison of multivariate curve resolution and parallel factor analysis 2

Second-order liquid chromatographic data with multivariate spectral (UV–vis or fluorescence) detection usually show changes in elution time profiles from sample to sample, causing a loss of trilinearity in the data. In order to analyze them with an appropriate model, the latter should permit a given component to have different time profiles in different samples. Two popular models in this regard are multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). The conditions to be fulfilled for successful application of the latter model are discussed on the basis of simple chromatographic concepts. An exhaustive analysis of the multivariate calibration models is carried out, employing both simulated and experimental chromatographic data sets. The latter involve the quantitation of benzimidazolic and carbamate pesticides in fruit and juice samples using liquid chromatography with diode array detection, and of polycyclic aromatic hydrocarbons in water samples, in both cases in the presence of potential interferents using liquid chromatography with fluorescence spectral detection, thereby achieving the second-order advantage. The overall results seem to favor MCR-ALS over PARAFAC2, especially in the presence of potential interferents.

Automated resolution of overlapping peaks in chromatographic data

Parallel factor analysis 2 (PARAFAC2) has been shown to be a powerful tool for resolution of complex overlapping peaks in chromatographic analyses. It is particularly useful because of its ability to handle shifts in the elution time mode and peak shape changes. Like all curve resolution techniques, PARAFAC2 will only find chemically meaningful parameters (elution time profiles and mass spectra) if the correct number of factors are determined. So far, the primary way to determine an appropriate number of factors, when using PARAFAC2, is to calculate models with different number of factors and then inspect the models manually. This approach is time consuming, and the result may be biased because of the manual assessment of the model quality, making PARAFAC2 inaccessible for analytical chemists in general. Here, we develop a method that can determine an appropriate number of factors in an automated way. The automation is based on a number of model diagnostics (quality criteria) collected from models with different numbers of factors. Combining these diagnostics, it is possible to assess what the appropriate number of components is. In this work, only gas chromatography–mass spectrometry data are considered. However, it will most likely be fairly straightforward to expand the work to also cover liquid chromatography data (with a multivariate detector). Automating the model quality evaluation of the PARAFAC2 model enables both the inexperienced and trained user to perform comprehensive and advanced analysis of chromatographic data with a minimum of manual work. © 2013 The Authors. Journal of Chemometrics Published by John Wiley & Sons Ltd.