Window Evolving Factor Analysis Research Articles

Local rank-based spatial information for improvement of remote sensing hyperspectral imaging resolution

This paper shows the effect of using local rank and selectivity constraints based on spatial information of spectroscopic images to increase the performance of Multivariate Curve Resolution (MCR) methods and to decrease the ambiguity of final results. Fixed Size Image Window-Evolving Factor Analysis (FSIW-EFA) is applied to discover which pixels are more suitable for the application of local rank constraints. An automated method to help in setting appropriate threshold values for the application of FSIW-EFA, based on global and local use of Singular Value Decomposition (SVD) is proposed. Additional use of correlation coefficients between selected reference spectra and pixel spectra of the image is shown to provide an alternative way for the application of the selectivity constraint in spectroscopic images for the first time. This alternative method resulted to be satisfactory when pure pixels exist.

Elimination of chromatographic and mass spectrometric problems in GC-MS analysis of Lavender essential oil by multivariate curve resolution techniques: Improving the peak purity assessment by variable size moving window-evolving factor analysis.

In analysis of complex natural matrices by gas chromatography-mass spectrometry (GC-MS), many disturbing factors such as baseline drift, spectral background, homoscedastic and heteroscedastic noise, peak shape deformation (non-Gaussian peaks), low S/N ratio and co-elution (overlapped and/or embedded peaks) lead the researchers to handle them to serve time, money and experimental efforts. This study aimed to improve the GC-MS analysis of complex natural matrices utilizing multivariate curve resolution (MCR) methods. In addition, to assess the peak purity of the two-dimensional data, a method called variable size moving window-evolving factor analysis (VSMW-EFA) is introduced and examined. The proposed methodology was applied to the GC-MS analysis of Iranian Lavender essential oil, which resulted in extending the number of identified constituents from 56 to 143 components. It was found that the most abundant constituents of the Iranian Lavender essential oil are α-pinene (16.51%), camphor (10.20%), 1,8-cineole (9.50%), bornyl acetate (8.11%) and camphene (6.50%). This indicates that the Iranian type Lavender contains a relatively high percentage of α-pinene. Comparison of different types of Lavender essential oils showed the composition similarity between Iranian and Italian (Sardinia Island) Lavenders.

A novel alternating least-squares method based on fixed region scanning evolving factor analysis (FRSEFA) and its application in process monitoring

A new method called fixed region scanning evolving factor analysis (FRSEFA) is proposed based on fixed-size moving window evolving factor analysis (FSMWEFA). In FRSEFA, a base set matrix Xbs that is a submatrix of the entire spectra data matrix X, corresponding to a special region in the time direction, is selected. Then, the base set Xbs combines a moving window xi containing only one time point to construct a submatrix Xt,i. A series of eigenvalues are obtained to accurately determine the starting time or ending point because the moving window contains only one time point, so that the problem of time shift in FSMWEFA can be solved. The combination of FRSEFA and alternating least squares (ALS) is utilized to determine the precise time of the transformation of components during the reaction and to obtain the profiles of concentration and spectrum of the components of interest in the mixture. Two real experimental data were studied by the developed algorithm. The results showed that the precise time of transformation could be obtained and spectrum and concentration profiles were also estimated, providing more useful information for reaction processes.

An Identification of the Growing Area of Longjing Tea Based on the Fisher's Discriminant Analysis with the Combination of Principal Components Analysis

In recent years, the fake Xihu Longjing Tea has damaged its brand image and reputation. This paper based on the Fisher's discriminant analysis using the fixed-size moving window evolving factor analysis to find characteristic spectra through analyzing the near infrared spectroscopy of Xihu Longjing Tea and Zhejiang Longjing Tea. The Fisher's discriminant analysis was used to reduce the data dimension combined with the principal component analysis. A discrimination model was set up for the identification of the Xihu Longjing Tea and Zhejiang Longjing Tea. The model's accuracy is 97.3%. The results proved that this model is feasible to identify the differences between the Xihu Longjing Tea and Zhejiang Longjing Tea. Unlike other methods, the tea does not need to be made into a powder. It also lays out a theoretical foundation for developing an identification instrument for Xihu Longjing Tea.

Chemometric resolution techniques combined with GC-MS to enhance determination of the volatile chemical constituents of bay leaves

The 71 constituents of essential oil (EO) of bay leaves were identified with gas chromatography-mass spectrometry (GC-MS) by applying a similarity search between the obtained mass spectra and database. This number was increased to 131 constituents with the help of different chemometric resolution techniques. Multivariate curve resolution-alternating least squares (MCR-ALS) is used to obtain pure chromatograms and mass spectra for the constituents present in each overlapping/embedded peaks cluster as well as their relative concentrations. Other chemometric methods such as simple to use interactive self-modeling mixture analysis (SIMPLISMA), morphological score (MS) and Fixed Size Moving Window Evolving Factor Analysis (FSMWEFA) were used to determine the number of constituents, pure variables, zero concentration and selective regions. The most important constituents of the Iranian bay leaves are linalool (12.31%), 1,8-cineole (11.38%), α-terpineol acetate (7.71%), eugenol methyl ether (6.87%) and α-phellandrene (4.30%). Despite previous studies, chemometric resolution techniques were implemented as a necessary step for the comprehensive analysis of the volatile constituents of bay leaves.

Analysis of the volatile chemical constituents in Mindium laevigatum by gas chromatography — Mass spectrometry and correlative chemometric resolution methods

The essential oil of Mindium laevigatum was extracted by applying simultaneous distillation extraction (SDE) method and studied with gas chromatography–mass spectrometry (GC–MS). The whole of 61 constituents was identified by applying similarity search between the obtained mass spectra and database. This number was expanded to 91 using multivariate curve resolution — alternation least square (MCR–ALS) method. Different chemometric methods such as simple-to use interactive self-modeling mixture analysis (SIMPLISMA), morphological score (MS) and Fixed Size Moving Window Evolving Factor Analysis (FSMWEFA) were used for determining the number of constituents, pure variables, zero concentration and selective regions. Self‐modeling curve resolution (SMCR) was suggested for resolving the co-eluted GC–MS peak into pure chromatograms and mass spectra. MCR–ALS prosperously applied for this aim. Pure variables from SIMPLISMA were applied as initial mixing matrix in iterative process. The resolved mass spectra were properly identified applying mass spectral search in NIST and Wiley library. The outcomes of this work proved that the combination of hyphenated chromatographic methods and resolution techniques provides a complementary method for the exact analysis of essential oils.

Component correlation between related samples by using comprehensive two-dimensional gas chromatography–time-of-flight mass spectrometry with chemometric tools

A chemometric strategy has been developed to discover component difference and similarity between two chromatograms (correlation) by using comprehensive two-dimensional (2D) gas chromatography with time-of-flight mass spectrometry (GC×GC-TOFMS). It allows for rapid determination of the presence or absence of analytes of interest in both pure and overlapping peak clusters, and then locates elution windows of target components. First, representative elution windows of analytes are extracted from the 2D GC×GC map to characterize the spectral space and further construct an orthogonal projection matrix for analysis. Next, multi-component spectral correlative chromatography (MSCC) is employed to scan the whole or pre-selected GC×GC-TOFMS data range to obtain component features. An auto-correlative projection curve is proposed to assess the projection residual from MSCC by defining a new evaluation index as reference, based on fixed-size moving window evolving factor analysis. In principle, the method can also be utilized to locate specific compounds whose known spectra are available. It is not restricted by data with high homoscedastic and heteroscedastic noise. Simulated GC-MS data and an extremely complicated herbal product mixture comprising 9 herbs demonstrates that the two-dimensional correlative distribution graph is effective for chemical interpretation between GC×GC-TOFMS data. It allows discovery of information buried in this type of highly complex dataset, especially for rapid and effective data comparison, where specific molecular identity might otherwise be hidden.

Resolving batch chromatographic overlapping peaks of flavoring essence using stepwise key spectrum selection

Stepwise key spectrum selection (SKSS) was introduced to resolve batch overlapping peaks from gas chromatography–mass spectrometry (GC–MS) analysis of ten batch tobacco flavoring samples in different storage times. Resolution was implemented on a software platform that embedded the SKSS method. The data from GC–MS analysis of the samples were saved and prepared in ASCII files and then were inputted into the software platform for visual inspections. The data segment with overlapping peaks was precut for subsequent analysis. Spectral background in the data was removed using a linear fitting of the baseline. Four components in the overlapping peaks were automatically detected by the SKSS method. The resolution of the concentration profiles and spectra of the four components was conducted by setting only one parameter, the negative area ratio, as 0.01. The fixed size moving window evolving factor analysis and evolving factor analysis were applied to validate the resolved concentration profiles. The resolved mass spectra were validated by the searched standard through library search at the pure component regions revealed by the resolved concentration profiles. The results showed that the SKSS method could be a simple but powerful tool in resolving batch chromatographic overlapping peaks.

Quantitative analysis by resolving variation matrices of pH-Spectrophotometric titration data using Self-Modeling Curve Resolution.

A new method is proposed for resolving pH-spectrophotometric titration data to determine mixtures of monoprotic acids. The method uses variation matrices to circumvent the rank deficiency problem of such data by shifting to another target, namely the reaction space. Self-modeling curve resolution is used to resolve variation matrices of pH-spectrophotometric titration data for acid mixtures. The variation matrix is obtained by subtracting the zero-point spectrum (e.g., acidic spectrum) from each spectrum at each pH value. Mean-centering window evolving factor analysis is used to identify the local reaction map. Reaction spectra can be estimated using selective regions of the local reaction map, from which reaction extent vectors can be obtained by alternating least-squares optimization. It was shown that quantitative analysis can be performed by augmentation of the variation matrix of the unknown and standard samples and comparison of obtained reaction extent curves. The applicability of the proposed method was evaluated using model data for binary and ternary mixtures of monoprotic acids. pH-spectrophotometric titration data for real binary mixtures of tartrazine/sunset yellow were also investigated using the proposed method and their concentration were determined in a real sample.

Aza-Michael reaction with enone-modified vegetable oils: evidence of the keto–enolic equilibrium by NIR chemical imaging and evolving factor analysis

The existence of an enone-dienol tautomerism in enone-containing triglyceride, obtained from high oleic sunflower oil, was detected in an image set captured at 95 °C by fixed-size image window-evolving factor analysis. A (1)H NMR spectrum and a UV-Visible spectrum of the enone-containing triglyceride at 25 °C and at 95 °C were measured to corroborate the presence of the enol form. The presence of this equilibrium explains the different behaviour of the curing reaction between an enone-containing triglyceride and diaminodiphenylmethane, which was evaluated following the spectral evolution of two pixels that differ in the presence or absence of the enol form. As the enol form acts as a inert species in the reaction, it leads to different degree of advance depending on which growing zone is observed.

Assessment of the co-elution problem in gas chromatography-mass spectrometry using non-linear optimization techniques

Multivariate curve resolution based on the minimization of an objective function (MCR-FMIN) defined directly from the non-fulfillment of constraints was applied for the first time as a deconvolution method to separate co-eluted gas chromatographic-mass spectrometric (GC-MS) signals. Simulated and real (standard real mixture and limon oil) GC-MS data were used to evaluate the feasibility of this method. The MCR-FMIN solutions have been obtained based on the rotation of principal component analysis (PCA) solutions using the non-linear optimization algorithms. Calculation of the initial values of R rotation matrix using model free analysis methods such as fixed-size moving window-evolving factor analysis (FSMW-EFA), evolving latent projective graphs (ELPGs), and heuristic evolving latent projection (HELP) was proposed for faster convergence and avoiding to be stuck in local minima in MCR-FMIN algorithm. The band boundaries of feasible solutions (MCR-BANDS) obtained using MCR-FMIN were calculated for simulated data to assess the reliability of the method. In addition, the results of this method were compared with those of two most common self-modeling curve resolution (SMCR) methods of multivariate curve resolution-alternating least square (MCR-ALS) and HELP. A reasonable result can be obtained by selecting proper constraints, such as non-negativity, unimodality, normalization, and selectivity. However, when the number of components or the level of noise in each peak cluster increase, the convergence of algorithm becomes difficult and the results are not reliable. For quick and accurate analysis of co-eluted multi-component problematic GC-MS data MCR-FMIN can be considered as an alternative method to the MCR-ALS and HELP methods.

Parallel vector analysis based soft resolution of spectral data from pH‐metric titration using symmetry constraint

AbstractIn this study, a soft method is proposed to calculate concentration and spectral profiles for the two‐way spectral data from dissociation equilibria of polyprotic acids (HnA). This method has four main distinct steps: (i) a fixed size moving window evolving factor analysis (FSMWEFA) was used to identify the local rank map, (ii) WFA was applied to calculate the concentration profiles of HnA and An− (selection of the window for application of WFA was performed using EFA), (iii) PVA was used to calculate Hn − 1A to HA spectral profiles, and (iv) a symmetry constraint, in addition to the non‐negativity constraint, was utilized to obtain the unique concentration and spectral profiles from different acceptable sets of profiles. In the absence of any selective region in the spectral data, the proposed soft method resulted in unique solution without rotational ambiguity. This study is the first application of symmetry constraint on concentration profiles. The rotational ambiguity drastically decreased on considering the constraint of symmetry of the Hn − 1A and HA concentration profiles, in addition to non‐negativity of profiles. Simulated examples were used to confirm these approaches. Effect of closeness of dissociation constants on the estimated values of constants was investigated. The results showed that when the difference between pKa values is more than 1.2, the obtained errors in the estimation of pKa values are less than about 6.5%. The considered real data were from pH‐metric titration of fluorescein. The obtained spectral and concentration profiles and the estimated pKa values for fluorescein were in good agreement with the previously reported data. Copyright © 2009 John Wiley & Sons, Ltd.

Determination of the Volatile Oil of Magnolia biondii Pamp by GC–MS Combined with Chemometric Techniques

An optimized temperature-programmed gas chromatography–mass spectrometry system combined with chemometric methods was firstly applied to analyze the volatile components of M. biondii Pamp. A total of 65 components were identified using similarity searches between mass spectra and MS database. This number was extended to 80 components with the help of chemometric techniques. The peak purity of two-way data was controlled by fixed size moving window evolving factor analysis, two dimensional-evolving latent projection graph and three dimensional-evolving latent projection graph. Then the overlapped peak clusters were resolved using heuristic evolving latent projection. The results prove that the reported approach is powerful for the analysis of complex herbal samples.

Resolution of near-infrared spectral data from distillation of binary mixtures and calculation of band boundaries of feasible solutions for species profiles

In this work, mean centering, ordinary and incomplete rank annihilation based methods were applied to estimate concentration profiles (g/mL) and pure spectra of components from an evolutionary near infrared spectral data for successive condensates from distillation process of binary mixtures. Constraints such as non-negativity, selectivity of some spectral regions and density of condensates were applied during the resolution of some series of data. Fixed size moving window evolving factor analysis (FSMWEFA) and orthogonal projection analysis (OPA) were the applied chemometrics methods for assigning the selective regions. No pure spectrum from any of components or calibration samples was necessary for performing the analysis. Three binary mixtures containing toluene:n-hexane, toluene:cyclohexene and toluene:ethanol were investigated using the proposed method. Band boundaries of feasible solutions for pure absorption spectra and species concentration profiles for the mixture of components were successfully estimated in presence of high spectral overlap. In the first case the solution was unique, but in the second and third distillations a number of acceptable solutions were obtained as band boundaries.

Self-association of ( R)-1,3-butanediol in an inert dilute solution studied by infrared spectroscopy in combination with density functional theory and chemometrics

Self-association of ( R)-1,3-butanediol in a dilute carbon tetrachloride (CCl 4) solution was studied by infrared (IR) spectroscopy in combination with density functional theory (DFT), Sugeta’s nonlinear least square (NLS) method and chemometrics methods including fixed-size moving window evolving factor analysis (FSMWEFA), principal component analysis (PCA), simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), and iterative target transformation factor analysis (ITTFA). The association size of ( R)-1,3-butanediol in the CCl 4 solution estimated from PCA, SIMPLISMA and ITTFA are 3.2730, 3.2797 and 3.2950, respectively, suggesting that the major multimer species of ( R)-1,3-butanediol in the solution are trimers. A theoretical investigation of trimer structures of ( R)-1,3-butanediol was carried out with DFT. It was found from the DFT calculation that cyclic trimers are more stable than linear ones. Structure of hydrogen-bonded OH ring and position of side chains are the two main factors that determine the stability of trimers. The intra-molecular hydrogen bonded OH…OH structure in the ( R)-1,3-butanediol monomer brings additional influence on the trimers’ structures.

Study on multimers and their structures in molecular association mixture

Self-association system of ( R )-1,3-butanediol in dilute carbon tetrachloride (CCl 4 ) solution is studied as a model of molecular association mixture. Analysis methods including FSMWEFA (fixed-size moving window evolving factor analysis) combined with PCA (principal component analysis), SIMPLISMA (simple-to-use interactive self-modeling mixture analysis), and ITTFA (iterative target transformation factor analysis) are adopted to resolve infrared spectra of ( R )-1,3-butanediol solution. Association number and equilibrium constant are computed. ( R )-1,3-butanediol in dilute inert solution is determined as a monomer-trimer equilibrium system. Theoretical investigation of trimer structures is carried out with DFT (density functional theory), and structural factors are analyzed.

ImpuR: A Collection of Diagnostic Tools Developed inRin the Context of Peak Impurity Detection in HPLC-DAD but Potentially Useful with Other Types of Time-Intensity Matrices

HPLC-DAD systems generate time intensity (absorbance) matrices called spectrochromatograms. Under good experimental conditions, spectro-chromatograms of elution peaks of pure analytes are bilinear products of a time peak and an absorbance spectrum. Co-eluting impurities create deviations from this pure bilinear structure. Unfortunately, other imperfections, such as scan averaging, large optical windows, imperfect lamp alignment, mobile phase fluctuations, etc. also create departures from the pure bilinear structure. This makes it hard to distinguish low concentration impurities from artifacts and hampers safe detection of contaminants. There are two main ways to deal with such artifacts: removal and simulation, and ImpuR provides R functions to do both and to integrate both approaches. More specifically, ImpuR provides a set of tools to explore time-intensity matrices with respect to their bilinear structure and departures from it. It includes exploratory graphs for bilinear matrices (bilinear residual graphs and singular value decompositions), spectral dissimilarity curves via window-evolving factor analysis with heteroscedasticity correction and the sine method, methods for removal of artifacts, and a comprehensive simulation tool to assess the impact of potential artifacts and to allow for the construction of guide curves for use with the sine method.

A criterion for evaluation of chromatographic separation efficiency based on chemometric data treatment: Peak-purity weighted resolution

In this paper, a novel resolution criterion for evaluating chromatographic peak-purity and separation efficiency of complicated mixtures is suggested. In contrast to most conventional criteria, which are defined on the chromatograms recorded by single response detectors, the proposed criterion, peak-purity weighted resolution (PPWR), evaluates the resolution by considering the number of co-eluted pure components, an information which can be easily extracted from two-dimensional chromatography–spectrometry data by chemometric methods, such as evolving factor analysis (EFA) and fixed-size moving window evolving factor analysis (FSMWEFA). As demonstrated by simulated and experimentally recorded data, PPWR can not only give an overall evaluation of separation quality, but also can provide reliable information for purity assessment of a limited number of interested components.

Resolution of multicomponent overlapped peaks: A comparison of several curve resolution methods

Several curve resolution methods were compared in their performance of identification and quantification of overlapping peaks. These resolution methods are heuristic evolving latent projections (HELP), sub-window factor analysis (SFA), and orthogonal projection resolution (OPR). In this paper, HELP, SFA and OPR with the rank map produced by evolving factor analysis (EFA) or fixed size moving window-evolving factor analysis (FSMW-EFA) were applied to the simulated and experimental data. The resolved results were compared qualitatively and quantitatively. In addition, the further comparison was carried out with the results obtained from multivariate curve resolution-alternate least square (MCR-ALS) by using the initial estimates provided by EFA.

Characterization of essential oil components of Iranian geranium oil using gas chromatography–mass spectrometry combined with chemometric resolution techniques

The essential oil components of geranium oil cultivated in center of Iran were identified and determined using gas chromatography–mass spectrometry data combined with the chemometric resolution techniques. A total of 61 components accounting for 91.51% were identified using similarity searches between the mass spectra and MS database. This number was extended to 85 components using chemometric techniques. Various chemometric methods such as morphological scores, simplified Borgen method (SBM) and fixed size moving window evolving factor analysis (FSMWEFA) were used for determining the number of components, pure variables, zero concentration and selective regions. Then the overlapping peak clusters were resolved into pure chromatograms and pure mass spectra using heuristic evolving latent projections (HELP) method. A characteristic feature of the Iranian geranium oil is the absence of 10- epi-γ-eudesmol in its constituents compared with the oil from northern and southern parts of India. The results of this work show that combination of hyphenated chromatographic methods and resolution techniques provide a complementary method for accurate analysis of essential oils.