Fixed Size Moving Window Evolving Factor Analysis Research Articles

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.

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.

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.

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.

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.

Local resolution of two-way data from multicomponent equilibria

A self-modeling curve resolution (SMCR) method is proposed to calculate concentration and spectral profiles for the two-way spectral data from an equilibrium containing several chemical components. The proposed method has three main distinctive steps: (i) fixed size moving window evolving factor analysis (FSMWEFA) is used to identify the selective and zero concentration regions for a desired component, (ii) orthogonal projection resolution (OPR) is used to calculate its concentration profile and (iii) the component striping is done directly to resolve other components. The results of simulated and real polyprotic acid dissociation equilibria showed that the proposed combined method performs well even in situation when the successive stepwise equilibrium constants are close to each other. The applicability of method for resolving the triprotic acid system with rank deficiency due full spectral overlapping of two involved chemical species also is shown.

Exploring Time-Dependent Structural Changes during the Cold Crystallization Process of Isotactic Polystyrene by Infrared Spectroscopy and Multivariate Curve Resolution

The present study attempts an application of Fourier transform infrared (FT-IR) spectroscopy in conjunction with multivariate curve resolution (MCR) techniques to explore the structural evolution of isotactic polystyrene (iPS) during the cold crystallization process. The focus of the present study is placed on the performance of MCR techniques, e.g., orthogonal projection (OP), alternating least squares (ALS), and fixed-size moving window evolving factor analysis (FSMWEFA), and the interpretability of spectral changes in the investigated chemical process. As a result, valuable information and conclusions about the structural evolution of iPS during the crystallization process can be extracted: when the amorphous phase of iPS changes, the ordering of the phenyl rings takes place first, and then the polymer chains adjust their local conformations to form short 3(1) helix structures. Furthermore, according to intensity profiles of the spectral variations, the ordering of the phenyl rings proceeds more intensely than the formation of ordered local chains, and the structural evolution of iPS occurs even during the induction period. The spectral variations resulting from the conformational changes in the 3(1) helical structures depend on the sequence length of the helical chains: the longer the polymer chain is, the smaller the corresponding band variations are. It has been demonstrated that the combination of FTIR spectroscopy and chemometric MCR techniques is very promising for the analysis of the crystallization process of polymers. MCR is a powerful tool for analyzing and visualizing spectral data and integrating them with other information, making spectral intensity variations more amenable to interpretation in order to explore the molecular dynamics of polymers.

Comparing chemical fingerprints of herbal medicines using modified window target-testing factor analysis

A "chromatographic fingerprint" of a herbal medicine is essentially its chromatographic spectrum: a characteristic representation of its chemical components, some of which are pharmacologically active. Since a wide variety of factors, such as the geographical location, the harvest season, and the part used can influence the chemical constituents (and therefore the pharmacological activity) of any particular herbal medicine and its products, these fingerprints provide a way to compare and contrast the compositions of different variants of the same herbal medicine. In particular, it is possible to ascertain whether particular components present in one herbal fingerprint are also present in another fingerprint. In this work we use a novel method-modified window target-testing factor analysis (MWTTFA), based on the use of target factor analysis (TFA), fixed-size moving window evolving factor analysis (FSMWEFA) and a Gaussian shape correction to the chromatographic profiles-to achieve this end. To demostrate the strategy, the fingerprints of samples from garlics produced in different geographical locations were compared, as well as the fingerprints of samples taken from above-ground and below-ground parts of Houttuynia cordata Thunb. The results from these comparisons clearly show that four chemical components present in Hunan common edible garlic are absent in Xingping base garlic, while seven components are present in Xingping base garlic but absent in Hunan common edible garlic. Also, eleven components are present in the sample from the above-ground part of Houttuynia cordata Thunb but not in the sample from the below-ground part, while seven components are present in the sample from the below-ground part of Houttuynia cordata Thunb that are not present in the sample from the above-ground part. These interesting conclusions should be very useful for future pharmacological and clinical research into these herbal medicines, and the novel MWTTFA technique can also be used for quality control purposes.

Analyzing of the volatile chemical constituents in Artemisia capillaris herba by GC–MS and correlative chemometric resolution methods

The volatile chemical constituents in traditional Chinese medicine (TCM), Artemisia capillaris herba, were determined by gas chromatography–mass spectrometry (GC–MS). The acquired two-dimensional data were resolved by correlative chemometric resolution methods. The noise in the raw data is pretreated by roughness penalty smoothing method. With the data denoised, heteroscedastic noise and signal-to-noise ratio were decreased apparently, which was favorable to the determination of component number. The selective range can be extracted from rankmap obtained by fixed size moving window evolving factor analysis (FSMWEFA) conveniently. The overlapped chromatographic peaks were resolved into pure chromatograms and pure spectra with evolving window orthogonal projection (EWOP). The purity of the resolved pure spectra were improved furthermore with the heteroscedastic noise decreased through roughness penalty smoothing method, although the basic structure of the raw data changes little. Qualitative analysis was performed by similarity search in NIST147 and Willey library. Pure chromatograms are in favor of quantitative analysis, which was obtained by total volume integration. Forty-two of seventy-five separated constituents in essential oil, accounting for 89.03% of the total content, were identified. The result proves the combined approaches to be powerful for the analysis of complex herbal samples.

Chemometric resolution of ATR-IR spectra data for polycondensation reaction of bis(hydroxyethylterephthalate) with a combination of self-modeling curve resolution (SMCR) and local rank analysis.

Self-modeling curve resolution (SMCR) methods, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) and alternating least squares (ALS) were used to calculate pure concentration profiles and pure spectra for the two-way spectral data collected during the on-line polycondensation reaction of bis(hydroxyethylterephthalate) with an ATR-FT-IR spectrometer. In order to improve the resolution results, SIMPLISMA was combined with local rank analysis method, fixed size moving window evolving factor analysis (FSMWEFA) to search for selective regions of various components and then look for the purest wavenumber variables in the selective regions. Such combination allows more accurate determination of the number of chemical components in the reaction system and the calculations of more accurate concentration profiles and spectra.