Mitigating model deficiency in three-way data analysis by the combination of background constraining and iterative correcting techniques

PARAFAC is a popular model for trilinear data analysis in analytical chemistry. The prerequisite for the successful application of PARAFAC in analytical chemistry is that the three-way data array should follow a trilinear model, which is always violated by the presence of deviations such as Rayleigh scattering in fluorescence spectroscopy. In order to mitigate the influence of model deviations, background constraining and iterative correcting techniques are advocated in this contribution. The method established on these two techniques can nearly eliminate the effect of model deviation on the chemical loading parameters estimated. Compared with other methods for mitigating model deviations, the proposed method requires no prior knowledge about the chemical loading parameters. It is also unnecessary to assign weights to data entities as the weighted PARAFAC of Anderson does. Its implementation is comparable to PARAFAC-ALS and can be programmed to be completely automatic. Its performance has been demonstrated by fluorescent and chromatographic experiments.     

A PARAFAC algorithm using penalty diagonalization error (PDE) for three-way data array resolution

A modified parallel factors analysis (PARAFAC) algorithm with the penalty diagnolization error (PDE) was developed. This algorithm can overcome the slow convergence problem of the traditional PARAFAC method and is insensitive to the number of components, i.e., it is much faster than PARAFAC and insensitive to overestimation of the dimensionality of the model. The characteristic performance was demonstrated by treating simulated and real excitation-emission fluorescence data for samples of naphthalene, 1-naphthol and 2-naphthol with satisfactory results.     

Water-source characterization and classification with fluorescence EEM spectroscopy: PARAFAC analysis

Water-quality protection and environmental forensics require rapid water monitoring and source identification. In this paper, parallel factor analysis (PARAFAC) of fluorescence excitation-emission matrix spectra (EEMS) was used to characterize and classify water samples from landfills, wastewater treatment plants, lakes, and rivers. The study showed that the optimal number of components was four to represent the data set. The fluorescence fingerprints for water samples from different sources were sufficiently different, so qualitative water classification could be achieved. Specifically, Component 1 was the major fluorescing centre in river waters, with characteristics consistent with humic-like fluorophores; Component 2 was the dominant fluorophore in the treated wastewaters; Component 3 was the characteristic fluorophore in landfill leachates; and Components 1, 3, and 4 existed in lake waters at comparable weight, among which Component 4 may be considered as a protein- or amino acid-like fluorophore.     

A fully robust PARAFAC method for analyzing fluorescence data

Parallel factor analysis (PARAFAC) is a widespread method for modeling fluorescence data by means of an alternating least squares procedure. Consequently, the PARAFAC estimates are highly influenced by outlying excitation–emission landscapes (EEM) and element‐wise outliers, like for example Raman and Rayleigh scatter. Recently, a robust PARAFAC method that circumvents the harmful effects of outlying samples has been developed. For removing the scatter effects on the final PARAFAC model, different techniques exist. Newly, an automated scatter identification tool has been constructed. However, there still exists no robust method for handling fluorescence data encountering both outlying EEM landscapes and scatter. In this paper, we present an iterative algorithm where the robust PARAFAC method and the scatter identification tool are alternately performed. A fully automated robust PARAFAC method is obtained in that way. The method is assessed by means of simulations and a laboratory‐made data set. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of unfold principal component analysis and parallel factor analysis to the exploratory analysis of olive oils by means of excitation-emission matrix fluorescence spectroscopy

Discrimination between virgin olive oils and pure olive oils is of primary importance for controlling adulterations. Here, we show the potential usefulness of two multiway methods, unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of the two types of oils. We applied both methods to the excitation-emission fluorescence matrices (EEM) of olive oils and then compared the results with the ones obtained by multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. For U-PCA and PARAFAC, the ranges studied were λ_ex=300-400 nm, λ_em=400-695 nm and λ_ex=300-400 nm, λ_em=400-600 nm. The first range contained chlorophylls, whose peak was much more intense than those of the rest of species. The second range did not contain the chlorophylls peak but only the fluorescence spectra of the remaining compounds (oxidation products and Vitamin E). The three-component PARAFAC model on the second range was found to be the most interpretable. With this model, we could distinguish well between the two groups of oils and we could find the underlying fluorescent spectra of three families of compounds.     

Excitation-emission matrix fluorescence spectroscopy in conjunction with multiway analysis for PAH detection in complex matrices

A field portable, single exposure excitation-emission matrix (EEM) fluorometer has been constructed and used in conjunction with parallel factor analysis (PARAFAC) to determine the sub part per billion (ppb) concentrations of several aqueous polycyclic aromatic hydrocarbons (PAHs), such as benzo(k)fluoranthene and benzo(a)pyrene, in various matrices including aqueous motor oil extract and asphalt leachate. Multiway methods like PARAFAC are essential to resolve the analyte signature from the ubiquitous background in environmental samples. With multiway data and PARAFAC analysis it is shown that reliable concentration determinations can be achieved with minimal standards in spite of the large convoluting fluorescence background signal. Thus, rapid fieldable EEM analyses may prove to be a good screening method for tracking pollutants and prioritizing sampling and analysis by more complete but time consuming and labor intensive EPA methods.     

Competitive interaction of the antitumor drug daunorubicin and the fluorescence probe ethidium bromide with DNA as studied by resolving trilinear fluorescence data: the use of PARAFAC and its modification

The competitive interaction with DNA of daunorubicin (DR), being present in the clinical anti-tumor drug daunoblastina, and the fluorescence probe ethidium bromide (EB) has been studied by parallel-factor analysis (PARAFAC) and full-rank parallel-factor analysis (FRA-PARAFAC) of a fluorescence excitation-emission three-way data array. The PARAFAC algorithm can furnish stable resolution results for the data array studied, if the estimated number of chemical components is consistent with the real number. The FRA-PARAFAC algorithm is not sensitive to the estimated number of components of the fluorescence data array if the estimated number is not less than the real number. Both algorithms gave identical resolution for the three components concerned DR, EB, and the complex EB-DNA. Variations of the equilibrium concentrations of free DR, EB, and the complex EB-DNA were resolved by both algorithms. Experimental observation confirms the hypothesis that DR is an intercalator of DNA and that the binding interactions of DR and EB with DNA are a pair of parallel competitive intercalation reactions on same base sites of DNA. The method exemplified by this study provides a useful approach for studying competitive interactions of different drugs with DNA in the presence of interferents.     

Three- and four-way parallel factor (PARAFAC) analysis of photochemically induced excitation-emission kinetic fluorescence spectra

Independently emerging fluorescence profiles of unknown, photochemically induced degradation products of several naturally non-fluorescent pesticides were monitored using single exposure excitation-emission fluorescence spectroscopy. Three-way parallel factor analysis (PARAFAC) was employed to uniquely resolve the pure fluorescent spectra of the overlapping photolysis products. The quantitative utility of EEM photolysis-based determinations was demonstrated by employing four-way PARAFAC models built from EEM time cubes of multiple fenvalerate samples. The 4-way PARAFAC models were then used to predict original pesticide concentrations resulting in conservative limit of detection and root mean square errors of calibration (RMSEC) of 3 microM each.     

Advances in surface-enhanced Raman spectroscopy for analysis of pharmaceuticals: A review

Recently, Raman spectroscopy become a popular and potential analytical technique for the analysis of pharmaceuticals as a result of its advancement. The innovation of laser technology, Fourier Transform-Raman spectrometers with charge coupled device (CCD) detectors, ease of sample preparation and handling, mitigation of sub-sampling problems using different geometric laser irradiance patterns and invention of different optical components of Raman spectrometers are contributors of the advancement of Raman spectroscopy. Transmission Raman Spectroscopy is a useful tool in pharmaceutical analysis to address the problems related with sub-sampling in conventional Raman back scattering. More importantly, the development of surface-enhanced Raman scattering (SERS) has been a prominent advancement for Raman spectroscopy to be applied for pharmaceuticals analysis as it avoids the inherent insensitivity and fluorescence problems. As the active pharmaceutical ingredients (APIs) contain aromatic or conjugated domains with strong Raman scattering activity, Raman spectroscopy is an attractive alternative conventional analytical method for pharmaceuticals. Coupling of Raman spectroscopy with separation techniques is also another advancement applied to reduce or avoid possible spectral interferences. Therefore, in this review, transmission Raman spectroscopy, SERS, and SERS coupled with various separation techniques for pharmaceutical analysis are presented.     

Application of multi-way data analysis on excitation-emission spectra for plant identification

The ability to distinguish among diets fed to Damascus goats using excitation-emission luminescence spectra was investigated. These diets consisted of Medicago sativa L. (alfalfa), Trifolium spp. (clover), Pistacia lentiscus, Phyllirea latifolia and Pinus brutia. The three-dimensional luminescence response surface from phosphate buffered saline (PBS) extracts of each material was analyzed using muti-way analysis chemometric tools (MPCA) and parallel factor analysis (PARAFAC). Using three principal components, the spectra from each diet material were distinguished. Additionally, fecal samples from goats fed diets of either alfalfa or clover hays were investigated. The application of MPCA and PARAFAC to these samples using models derived from the pre-digested diet materials was strongly suggestive of the utility of similarly derive training samples for the elucidation of botanical diet composition for animals.     

Multiway chemometric decomposition of EEM of fluorescence of CdTe quantum dots obtained as function of pH

The effect of the pH (from 3 to 10) on the excitation emission matrices (EEMs) of fluorescence of CdTe quantum dots (QDs), capped with mercaptopropionic acid (MPA), were analyzed by multiway decomposition methods of parallel factor analysis (PARAFAC), a variant of the parallel factor analysis method (PARAFAC2) and multivariate curve resolution alternating least squares (MCR-ALS). Three different sized CdTe QDs with emission maximum at 555 nm (QDa), 594 nm (QDb) and 628 nm (QDc) were selected for analysis. The three-way data structures composed of sets of EEMs obtained as function of the pH (EEMs, pH) do not have a trilinear structure. A marked deviation to the trilinearity is observed in the emission wavelength order—the emission spectra suffers wavelength shift as the pH is varied. The pH-induced variation of the fluorescence properties of QDs is described with only one-component PARAFAC2 or MCR-ALS models—other components are necessary to model scattering and/or other background signals in (EEMs, pH) data structures. Bigger sized QDs are more suitable tools for analytical methodologies because they show higher Stokes shifts (resulting in simpler models) and higher pH range sensitivity. The pH dependence of the maximum wavelength of the emission spectra is particularly suitable for the development of QDs/EEMs wavelength-encoded pH sensor bioimaging or biological label methodologies when coupled to multiway chemometric decomposition.     

Capability of detection and three-way data

Due to the possibility of making analytical determinations in the presence of non-modelled interferents and to identify the analyte of interest, calibrations based on scores of PARAFAC decomposition of three-way data are becoming increasingly important in routine analysis.Furthermore, the IUPAC and EU (European Decision 2002/657/EC) have accepted the definition given by the ISO 11843 for the capability of detection as the minimum net quantity detectable with a pre-set probability of false positive and false negative. What is more, recently our research group has generalised this definition of capability of detection, CCβ, to multivariate calibrations. In practice, CCβ is a good measure of the quality of the calibration because in its definition it brings together analytical sensitivity with precision in analytical determinations.This paper studies the effect of the pre-treatment of the sample, the signal/noise ratio and the second-order advantage on CCβ when using second-order signals modelled by PARAFAC. All of them are experimental factors which influence the quality of the calibration. Analytical pre-treatment is habitual in the analysis of real samples. Specifically, we analyse the effect of the extraction phase and the clean-up of milk samples on the determination of chlortetracycline by HPLC-DAD. It is shown that it is more efficient to do the joint PARAFAC decomposition of the pure standards with the milk samples.Secondly, the effect of asymmetry on CCβ, according to the path of the noise of the signals, is studied. Specifically, in the determination of naphthalene by excitation-emission spectroscopy, EEM, it is the emission spectrum which limits the capability of detection. It is shown that by eliminating the spectra with the poorest signal/noise ratio in this path, the capability of detection can be substantially improved.Thirdly, the impact on CCβ when the second-order advantage is used, that is when PARAFAC calibration is used over samples with an unknown interference not modelled in the calibration step. This is important to apply a PARAFAC calibration to routine analysis in the IUPAC and European Decision framework. Specifically, in the determination of enrofloxacine in poultry feeding water through excitation-emission fluorescence CCβ is evaluated when the PARAFAC is built only with calibration samples or with the calibration samples plus the test samples with uncalibrated and unknown interferent.     

Simultaneous analysis of the photocatalytic degradation of polycyclic aromatic hydrocarbons using three-dimensional excitation-emission matrix fluorescence and parallel factor analysis

Polycyclic aromatic hydrocarbons (PAHs) may be photochemically degraded. Monitoring of degradation process of PAHs is carried out by traditional methods, which normally imply time-consuming procedures that do not allow the chemical process to be analyzed in real time. In the present study, photodegradation kinetics of dibenz[a,h]anthracene, benz[a]anthracene, benz[a]pyrene and benz[k]fluorantene were investigated in aqueous solutions under different conditions. A 2³ factorial design was used for optimizing the degradation process.Fluorescence spectroscopy is a fast, cheap and sensitive analytical method, attractive for use in conjunction with chemometric methods; in this case three-way analytical methodology based on fluorescence excitation-emission matrix (EEM) and parallel factor analysis (PARAFAC) was employed. A four-factor PARAFAC model made it possible to resolve the species presents in the degradation mixture and quantify the relative concentration of the analytes throughout the degradation. Several different parameters, such as core consistency, percentage of fit and correlation coefficients between recovered and reference spectra were employed to determine the suitable number of factors for the PARAFAC model. This new methodology allows us to determine satisfactorily the PAHs concentration during the photodegradation in mixtures of arbitrary composition, representing an interesting alternative to the conventional techniques normally used for the monitoring of degradation reactions.     

Determination of phenol in the presence of its principal degradation products in water during a TiO2-photocatalytic degradation process by three-dimensional excitation-emission matrix fluorescence and parallel factor analysis

This paper describes a simple and rapid way of monitoring a photocatalytic degradation of phenol in aqueous suspensions of TiO₂. A three-way analytical methodology based on fluorescence excitation-emission matrix (EEM) and parallel factor analysis (PARAFAC) was developed to resolve the species present in the reaction mixture and quantify the concentration of phenol and its principal degradation products throughout the degradation. Parameters such as core consistency, fit% and correlation coefficients between recovered and pure spectra were used to determine the appropriate number of factors for the PARAFAC model. The accuracy of the model was evaluated by the root mean square error of prediction (RMSEP). Using a four-factors PARAFAC model, phenol, hydroquinone, resorcinol and catechol, were satisfactorily determined. The proposed method is an interesting alternative to the traditional techniques normally used for monitoring degradation reactions.     

Determination of atenolol in human urine by emission-excitation fluorescence matrices and unfolded partial least-squares with residual bilinearization

A second-order multivariate calibration method based on a combination of unfolded partial least-squares (U-PLS) with residual bilinearization (RBL) has been applied to second-order data obtained from excitation-emission fluorescence matrices for determining atenolol in human urine, even in the presence of background interactions and fluorescence inner filter effects, which are both sample dependent. Atenolol is a cardioselective beta-blocker, which is considered a doping agent in shoot practice, so that its determination in urine can be required for monitoring the drug. Loss of trilinearity due to analyte-background interactions which may vary between samples, as well as inner filter effects, precludes the use of methods like parallel factor analysis (PARAFAC) that cannot handle trilinearity deviations, and justifies the employment of U-PLS. Successful analysis required to include the background in the calibration set. Unexpected components appear in new urine samples, different from those used in calibration set, requiring the second-order advantage which is obtained from a separate procedure known as residual bilinearization (RBL). Satisfactory results were obtained for artificially spiked urines, and also for real urine samples. They were statistically compared with those obtained applying a reference method based on high-performance liquid chromatography (HPLC).     

The application and comparison of several chemometric methods of excitation-emission matrix spectra in studying the interactions of metal complexes with DNA

The interactions of fs DNA and two metal complexes [Cu(phen)SO₄]·2H₂O and [Ni(phen)SO₄]·2H₂O were explored by several chemometric methods, including parallel factor (PARAFAC), singular value decomposition-least squares (SVD-LS), and singular value decomposition-nonnegative least squares (SVD-NNLS) of excitation-emission matrix spectra (EEMs). The applications of SVD-LS and SVD-NNLS in this domain have been discussed. Rayleigh scatter part is avoided by ordered zero and reconstructed by linear interpolation. The importance of avoiding Rayleigh scatter has also been discussed. All the three methods do well in qualitative analysis. SVD-LS does best in present small changes of ethidium bromide (EB). In order to get accurate results, PARAFAC and SVD-NNLS can be utilized together in quantitative analysis. All the three chemometric methods indicate that the DNA binding modes of [Cu(phen)SO₄]·2H₂O are hydrogen bond effect and intercalation, while intercalation is the only DNA binding mode for [Ni(phen)SO₄]·2H₂O. These results are verified by the electronic absorption and emission fluorescence spectra. Just like PARAFAC, both SVD-LS and SVD-NNLS are proven to be convenient and convincing in studying the interactions between nucleic acids and complexes.     

Strategies for solving matrix effects in the analysis of sulfathiazole in honey samples using three-way photochemically induced fluorescence data

A widely employed compound for honey treatment, sulfathiazole (ST), was determined in commercial honey samples, employing a combination of photochemically induced fluorescence excitation-emission matrices (EEMs) and chemometric processing of the recorded second-order data. Parallel Factor Analysis (PARAFAC) and Self-Weighted Alternating Trilinear Decomposition (SWATLD) methods were used for calibration. An appropriately designed calibration with a set of standards composed of 18 samples, coupled to the use of the second-order advantage offered by the applied chemometric techniques, allowed quantitation of sulfathiazole in spiked commercial honey samples. No previous separation or sample pretreatment steps were required. The results were compared with other calibration methods such as N-PLS and PLS-1 that produced good results on synthetic samples but not on the investigated commercial honey samples.     

Spectrofluorimetric studies on the binding of salicylic acid to bovine serum albumin using warfarin and ibuprofen as site markers with the aid of parallel factor analysis

The interactions of salicylic acid (SL) and two different site markers (warfarin for site I and ibuprofen for site II) with bovine serum albumin (BSA) in pH 7.4 Tris–HCl buffer have been investigated with the use of spectrofluorimetry. An equilibrium solution of BSA and SA was titrated separately with the two markers. This initial work showed that the binding of SL with BSA could be quite complex, and that there was probably a competitive interaction occurring between ibuprofen and SL. However, the spectral results were difficult to interpret clearly for the interaction of warfarin and SL in similar circumstances.

To extract more information from the resolution of fluorescence excitation-emission spectra, the contour plots of the fluorescence spectra indicated that the optimal excitation wavelengths for BSA, SL, warfarin and ibuprofen were different, and were found to be at 278, 295, 306 and 218 nm, respectively. The spectral information was arranged into three-way excitation-emission fluorescence matrix (EEM) stack arrays, and was submitted for analysis by the parallel factor analysis (PARAFAC) algorithm. Firstly, it was demonstrated that the estimated excitation and emission spectral responses for SL, BSA and the site markers, warfarin and ibuprofen, agreed well with the measured spectra. Then, the interpretation of the plots of simultaneously extracted (by PARAFAC) equilibrium concentrations for the above four reactants, showed that: (i) the SL primarily appears to bind in site I but at a different location from the high-affinity binding site (HAS) for warfarin, and the interaction partially overlaps with the low-affinity binding site (LAS) for warfarin. (ii) The SL may have two LAS—one in site II where the HAS for ibuprofen is located, and the other in site I at the LAS for ibuprofen. Thus, application of the PARAFAC method for the study of competitive interaction of SL and BSA with the aid of two different site markers has extracted information unobtainable by traditional methods such as the Scatchard plot, and provided useful means of data visualization.     

Second-order calibration of excitation-emission matrix fluorescence spectra for determination of glutathione in human plasma

A rapid non-separative spectroflourimetric method based on the second-order calibration of the excitation-emission data matrix was proposed for the determination of glutathione (GSH) in human plasma. In the phosphate buffer solution of pH 8.0 GSH reacts with ortho-phthaldehyde (OPA) to yield a fluorescent adduct with maximum fluorescence intensity at about 420 nm. To handle the interfering effects of the OPA adducts with aminothiols other than GSH in plasma as well as intrinsic fluorescence of human plasma, parallel factor (PARAFAC) analysis as an efficient three-way calibration method was employed. In addition, to model the indirect interfering effect of the plasma matrix, PARAFAC was coupled with standard addition method. The two-component PARAFAC modeling of the excitation-emission matrix fluorescence spectra accurately resolved the excitation and emission spectra of GSH, plasma (or plasma constituents). The concentration-related PARAFAC score of GSH represented a linear correlation with the concentration of added GSH, similar to that is obtained in simple standard addition method. Using this standard addition curve, the GSH level in plasma was found to be 6.10 ± 1.37 μmol L⁻¹. The accuracy of the method was investigated by analysis of the plasma samples spiked with 1.0 μmol L⁻¹ of GSH and a recovery of 97.5% was obtained.