Multivariate Calibration Algorithms Research Articles

Ensemble Multivariate Calibration Based on Mutual Information for Food Analysis Using Near-Infrared Spectroscopy

An ensemble multivariate calibration algorithm, termed as MISEPLS, is proposed. In MISEPLS, when constructing a member model, the variables that have mutual information (MI) with the response less than a threshold are eliminated; thus, the modeling can be performed in a subset of original variables and some problems arising from multi-collinearity can be avoided. Through experiments on three near-infrared (NIR) spectroscopic datasets from the food industry, MISEPLS proves to be superior to the single-model full-spectrum PLS and MIPLS (PLS combined with MI-induced variable selection). MISEPLS can improve the accuracy and robustness of a calibration model, without increasing its complexity.

Time-alignment of bidimensional chromatograms in the presence of uncalibrated interferences using parallel factor analysis: Application to multi-component determinations using liquid-chromatography with spectrofluorimetric detection

A new methodology for the alignment of matrix chromatographic data is proposed, based on the decomposition of a three-way array composed of a test and a reference data matrix using a suitably initialized and constrained parallel factor (PARAFAC) model. It allows one to perform matrix alignment when the test data matrix contains unexpected chemical interferences, in contrast to most of the available algorithms. A series of simulated analytical systems is studied, as well as an experimental one, all having calibrated analytes and also potential interferences in the test samples, i.e., requiring the second-order advantage for successful analyte quantitation. The results show that the newly proposed method is able to properly align the different data matrix, restoring the trilinearity which is required to process the calibration and test data with second-order multivariate calibration algorithms such as PARAFAC. Recent models including unfolded partial least-squares regression (U-PLS) and N-dimensional PLS (N-PLS), combined with residual bilinearization (RBL), are also applied to both simulated and experimental data. The latter one corresponds to the determination of the polycyclic aromatic hydrocarbons benzo[ b]fluoranthene and benzo[ k]fluoranthene in the presence of benzo[ j]fluoranthene as interference. The analytical figures of merit provided by the second-order calibration models are compared and discussed.

Second-order multivariate calibration procedures applied to high-performance liquid chromatography coupled to fast-scanning fluorescence detection for the determination of fluoroquinolones

Different second-order multivariate calibration algorithms, namely parallel factor analysis (PARAFAC), N-dimensional partial least-squares (N-PLS) and multivariate curve resolution-alternating least-squares (MCR-ALS) have been compared for the analysis of four fluoroquinolones in aqueous solutions, including some human urine samples (additional four fluoroquinolones were simultaneously determined by univariate calibration). Data were measured in a short time with a chromatographic system operating in the isocratic mode. The detection system consisted of a fast-scanning spectrofluorimeter, which allows one to obtain second-order data matrices containing the fluorescence intensity as a function of retention time and emission wavelength. The developed approach enabled us to determine eight analytes, some of them with overlapped profiles, without the necessity of applying an elution gradient, and thus significantly reducing both the experimental time and complexity. The study was employed for the discussion of the scopes of the applied second-order chemometric tools. The quality of the proposed technique coupled to each of the evaluated algorithms was assessed on the basis of the figures of merit for the determination of fluoroquinolones in the analyzed water and urine samples. Univariate calibration of four analytes led to limits of detection in the range 20–40 ng mL −1 and root mean square errors for the validation samples in the range 30–60 ng mL −1 (corresponding to relative prediction errors of 3–8%). The ranges for second-order multivariate calibration (using PARAFAC and N-PLS) of the remaining four analytes were: limit of detection, 2–8 ng mL −1, root mean square errors, 3–50 ng mL −1 and relative prediction errors, 1–5%.

When unfolding is better: unique success of unfolded partial least-squares regression with residual bilinearization for the processing of spectral–pH data with strong spectral overlapping. Analysis of fluoroquinolones in human urine based on flow-injection pH-modulated synchronous fluorescence data matrices

Synchronous fluorescence spectra measured in a flow-injection system with double pH gradient modulation constitute a new second-order signal which is herein studied for the quantitative determination of three fluoroquinolone antibiotics in spiked human urine samples. Because calibration is done using aqueous solutions of each of the three analytes ciprofloxacin, norfloxacin and ofloxacin, the fluorescent urine background makes it necessary to achieve the second-order advantage. Several second-order multivariate calibration algorithms were evaluated for this purpose: parallel factor analysis, unfolded and multiway partial least-squares with residual bilinearization, and multivariate curve resolution-alternating least-squares. The best analytical figures of merit, a root mean square error of 4-6 mg L(-1) (corresponding to a relative error of 4-6% for a calibration range from 0 to 200 mg L(-1) for each analyte), and a limit of detection of 4 mg L(-1) were obtained using partial least-squares (in the specific unfolded version) combined with residual bilinearization. Reasons for the improved success of this latter technique are provided on the basis of the analysis of simulated second-order data.

Second-order advantage from kinetic-spectroscopic data matrices in the presence of extreme spectral overlapping: A multivariate curve resolution—Alternating least-squares approach

Multivariate curve resolution coupled to alternating least-squares (MCR-ALS) has been employed to model kinetic-spectroscopic second-order data, with focus on the achievement of the important second-order advantage, under conditions of extreme spectral overlapping among sample components. A series of simulated examples shows that MCR-ALS can conveniently handle the studied analytical problem unlike other second-order multivariate calibration algorithms, provided matrix augmentation is implemented in the spectral mode instead of in the usual kinetic mode. The approach has also been applied to three experimental examples, which involve the determination of: (1) the antiparkinsonian carbidopa (analyte) in the presence of levodopa as a potential interferent, both reacting with cerium (IV) to produce the fluorescent species cerium (III) with different kinetics; (2) Fe(II) (analyte) in the presence of the interferent Zn(II), both catalyzing the oxidation of methyl orange with potassium bromate; and (3) tartrazine (analyte) in the presence of the interferent brilliant blue, both oxidized with potassium bromate, with the interferent leading to a product with an absorption spectrum very similar to tartrazine. The results indicate good analytical performance towards the analytes, despite the intense spectral overlapping and the presence of unexpected constituents in the test samples.

Doolittle multivariate calibration algorithm and analysis of W, Mo, Ti–SAF system

Being an accurate and stable algorithm, Doolittle Decomposition Algorithm (DDA) was first introduced into the chemistry field. The basic principle of Doolittle Multivariate Calibration Algorithm (DMCA) was investigated, and the chromogenic system of W, Mo, Ti–SAF with overlapping absorption peaks was analyzed by DMCA. The computational relative standard deviation with DMCA is within ± 8.0% which was better than the result of K-Matrix (within ± 10.0%), the comparison indicated the superiority of Doolittle Decomposition Algorithm in the concentration analyzing. It was demonstrated that DDA can avoid matrix inverting, reduce the orders of matrixes and speed up the operation of matrixes. So it has bright prospects in chemometrics.

Spectral in-situ analysis of NO2, NO3, COD, DOC and TSS in the effluent of a WWTP

An in-situ UV spectrometer was applied to the effluent of a WWTP in Switzerland and calibrated using a multivariate calibration algorithm based on PLS regression. Except for nitrite, the calibration was based on comparative measurements of the effluent in the plant laboratory. Samples made of stock solution added to three different matrices prepared in the EAWAG laboratory were used for the nitrite calibration because the effluent concentrations were always in the range of 0.06-0.26 mg/l. The results show very good precision for nitrite and nitrate. The measuring range for COD and DOC was not completely covered by the measurements, so the meaningfulness of the results is limited. Nevertheless the precision obtained for soluble COD is high enough for most applications at WWTPs. The accuracy of the TSS measurement is unsatisfactory as regards effluent limits since the spectrometer used does not cover the wavelength region up to 700 nm, which gives better signals for TSS calibration due to its strong correlation with turbidity.

Trace determination of carbendazim, fuberidazole and thiabendazole in water by application of multivariate calibration to cross-sections of three-dimensional excitation-emission matrix fluorescence.

The simultaneous determination of carbendazim, fuberidazole and thiabendazole was accomplished by cross-section (CS) fluorimetry in combination with multivariate calibration algorithms. The total luminescence information of the compounds was used to optimise the linear trajectories of the CS. A comparison between principal component regression (PCR) and two partial least squares (PLS) algorithms, PLS-1 and PLS-2, with different pre-processing methodologies was made. The final model, which applied the PLS-1 method, built using pesticide standard and emission spectra, was successfully used for the determination of these compounds in synthetic mixtures. However, a different PLS-1 multivariate calibration model, based on CS through the total luminescence spectroscopic data, was necessary for determining the cited pesticides in water samples. Mean centring was the best pre-processing technique in both PLS-1 models. This later calibration model was built from ultra-pure water samples spiked with known carbendazim, fuberidazole and thiabendazole concentrations, after solid-phase extraction (SPE). The method, which had a precision better than 5%, was shown to be suitable for carbendazim, fuberidazole and thiabendazole monitoring in water samples at trace levels.

Precision trace gas analysis by FT-IR spectroscopy. 2. The 13C/12C isotope ratio of CO2.

We report the development of a method of carbon stable isotope ratio analysis based on 1-cm-1 resolution Fourier transform infrared (FT-IR) spectroscopy, deployable in both laboratory and field applications. We demonstrate the determination of the 13C/12C ratio of CO2 (i.e., delta 13CO2) in air with an analytical precision of the order of +/- 0.1/1000 (i.e., +/- 0.01%). The FT-IR method relies on calibration using synthetically calculated absorbance spectra and a multivariate calibration algorithm. The method requires no sample preparation other than optional drying of the sample and may be applied directly to ambient air samples containing approximately 350 mumol mol-1 CO2 (molar mixing ratio). It may also be applied to samples more concentrated in CO2, such as human breath, approximately 5% CO2. We demonstrate the utility of the technique to the analysis of delta 13CO2 in air during an experimental field campaign and to the laboratory-based analysis of human breath. A similar method could also be used to determine the H/D ratio in atmospheric water vapor.

Precision trace gas analysis by FT-IR spectroscopy. 1. Simultaneous analysis of CO2, CH4, N2O, and CO in air.

We report the development of a method of trace gas analysis based on 1-cm-1 resolution Fourier transform infrared (FT-IR) spectroscopy, deployable in both laboratory and field applications. Carbon dioxide, methane, nitrous oxide, and carbon monoxide may be analyzed simultaneously in a single air sample using this method. We have demonstrated that the method can provide analytical precision of the order of +/- 0.15 mumol mol-1 for CO2, +/- 0.9 nmol mol-1 for CH4, +/- 0.3 nmol mol-1 for N2O, and +/- 0.3 nmol mol-1 for CO, expressed as mole fractions in dry air. The analytical precision is in all cases competitive with or superior to that of the more usual methods of analysis for these trace gases, namely, nondispersive infrared spectroscopy for CO2 and gas chromatography-based techniques for CH4, N2O, and CO. The novel FT-IR method relies on calibration using synthetically calculated absorbance spectra and a chemometric multivariate calibration algorithm, classical least squares.

Interpretive Spectroscopy for Near Infrared

ABSTRACT Qualitative and quantitative near infrared spectroscopic (NIRS) methods require the application of multivariate calibration algorithms to model NIR spectral response to chemical or physical properties of a calibration sample set. The identification of unique wavelength regions where changes in the response of the near infrared spectrometer are proportional to changes in the concentration of chemical components, or in the physical characteristics of samples under analysis is referred to as practical interpretive spectroscopy. Recent refinements of the NIR measurement technique include the emergence of chemometrics as a bona fide scientific discipline, and the diminishing distinction between near infrared, and infrared as measurement techniques. Rather the techniques are complementary, with each spectral region providing unique advantages for the analyst. This paper describes the use of classic infrared interpretive tools combined with chemometric tools for use in near infrared interpretive spectro...

Robust multivariate calibration algorithm based on least median of squares and sequential number theory optimization method

With the help of constraints on the concentrations to be estimated in direct multivariate calibration, an algorithm for least median of squares (LMS) was developed. The sequential number theory optimization (SNTO) method developed in statistics was used for robust multivariate calibration in order to reach the global optimization. The computational complexity of LMS is dramatically reduced by means of the constraints on the concentrations to be estimated and the SNTO method. The algorithm was applied to a simulated data set and to two sets of real data from two-and/or three-component analytical systems. Comparisons with the least squares technique show that the proposed method is efficient in terms of computational complexity and is robust to a large number of outliers in the data.

Noninvasive Blood Glucose Assay by Near-Infrared Diffuse Reflectance Spectroscopy of the Human Inner Lip

Near-infrared (NIR) spectra of the human inner lip were obtained by using a special optimized accessory for diffuse reflectance measurements. The partial-least squares (PLS) multivariate calibration algorithm was applied for linear regression of the spectral data between 9000 and 5500 cm−1 (Λ = 1.1–1.8 μm) against blood glucose concentrations determined by a standard clinical enzymatic method. Calibration experiments with a single person were carried out under varying conditions, as well as with a population of 133 different patients, with capillary and venous blood glucose concentration values provided. A genuine correlation between the blood glucose concentrations and the NIR-spectra can be proven. A time lag of about 10 min for the glucose concentration in the spectroscopically probed tissue volume vs. the capillary concentration can be estimated. Mean-square prediction errors obtained by cross-validation were in the range of 45 to 55 mg/dL. An analysis of different variance factors showed that the major contribution to the average prediction uncertainty was due to the reduced measurement reproducibility, i.e., variations in lip position and contact pressure. The results demonstrate the feasibility of using diffuse reflectance NIR-spectroscopy for the noninvasive measurement of blood glucose.

Mixture analysis of organic solvents using nonselective and nonlinear Taguchi gas sensors with artificial neural networks

This paper presents a protoytpe multicomponent gas and vapor analysis system consisting of eight nonselective and nonlinear Taguchi gas sensors, a temperature sensor, and multivariate calibration algorithms such as modified artificial neural netowrks. The application of this system to analyzing two- and three-component mixtures of benzene, toluene, acetone and trichloroethylene is demonstrated.