Mário César Ugulino de Araújo

The successive projections algorithm for variable selection in spectroscopic multicomponent analysis

Abstract The “Successive Projections Algorithm”, a forward selection method which uses simple operations in a vector space to minimize variable collinearity, is proposed as a novel variable selection strategy for multivariate calibration. The algorithm was applied to UV–VIS spectrophotometric data for simultaneous analysis of complexes of Co2+, Cu2+, Mn2+, Ni2+ e Zn2+ with 4-(2-piridilazo)resorcinol in samples containing the analytes in the 0.02–0.5 mg l−1 concentration range. A convenient spectral window was first chosen by a procedure also proposed here and applying Successive Projections Algorithm to this range allowed an improvement of the predictive capabilities of Principal Component Regression, Partial Least Squares and Multiple Linear Regression models using only 20% of the number of wavelengths. Successive Projections Algorithm selection resulted in a root mean square error of prediction at the test set of 0.02 mg l−1, while the best and worst realizations of a genetic algorithm used for comparison yielded 0.01 and 0.03 mg l−1. However, genetic algorithm took 200 times longer than Successive Projections Algorithm, and this ratio tends to increase dramatically with the number of wavelengths employed. Finally, unlike genetic algorithm, Successive Projections Algorithm is a deterministic search technique whose results are reproducible and it is more robust with respect to the choice of the validation set.

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.

Determination of total sulfur in diesel fuel employing NIR spectroscopy and multivariate calibration

A method for sulfur determination in diesel fuel employing near infrared spectroscopy, variable selection and multivariate calibration is described. The performances of principal component regression (PCR) and partial least square (PLS) chemometric methods were compared with those shown by multiple linear regression (MLR), performed after variable selection based on the genetic algorithm (GA) or the successive projection algorithm (SPA). Ninety seven diesel samples were divided into three sets (41 for calibration, 30 for internal validation and 26 for external validation), each of them covering the full range of sulfur concentrations (from 0.07 to 0.33% w/w). Transflectance measurements were performed from 850 to 1800 nm. Although principal component analysis identified the presence of three groups, PLS, PCR and MLR provided models whose predicting capabilities were independent of the diesel type. Calibration with PLS and PCR employing all the 454 wavelengths provided root mean square errors of prediction (RMSEP) of 0.036% and 0.043% for the validation set, respectively. The use of GA and SPA for variable selection provided calibration models based on 19 and 9 wavelengths, with a RMSEP of 0.031% (PLS-GA), 0.022% (MLR-SPA) and 0.034% (MLR-GA). As the ASTM 4294 method allows a reproducibility of 0.05%, it can be concluded that a method based on NIR spectroscopy and multivariate calibration can be employed for the determination of sulfur in diesel fuels. Furthermore, the selection of variables can provide more robust calibration models and SPA provided more parsimonious models than GA.

Classification of Brazilian soils by using LIBS and variable selection in the wavelet domain

This paper proposes a novel analytical methodology for soil classification based on the use of laser-induced breakdown spectroscopy (LIBS) and chemometric techniques. In the proposed methodology, linear discriminant analysis (LDA) is employed to build a classification model on the basis of a reduced subset of spectral variables. For the purpose of variable selection, three techniques are considered, namely the successive projection algorithm (SPA), the genetic algorithm (GA), and a stepwise formulation (SW). The use of a data compression procedure in the wavelet domain is also proposed to reduce the computational workload involved in the variable selection process. The methodology is validated in a case study involving the classification of 149 Brazilian soil samples into three different orders (Argissolo, Latossolo and Nitossolo). For means of comparison, soft independent modelling of class analogy (SIMCA) models are also employed. The best discrimination of soil types was attained by SPA-LDA, which achieved an average classification rate of 90% in the validation set and 72% in cross-validation. Moreover, the proposed wavelet compression procedure was found to be of value by providing a 100-fold reduction in computational workload without significantly compromising the classification accuracy of the resulting models.

Aspects of the successive projections algorithm for variable selection in multivariate calibration applied to plasma emission spectrometry

Abstract The successive projections algorithm (SPA) was recently proposed as a variable selection strategy to minimize collinearity problems in multivariate calibration. Although SPA has been successfully applied to UV–VIS spectrophotometric multicomponent analysis, no evidence of its ability to deal with variable sets with both high and low signal-to-noise ratios has been presented. This issue is addressed by the present work, which applies SPA to the simultaneous determination of Mn, Mo, Cr, Ni and Fe using a low-resolution plasma spectrometer/diode array detection system. This problem is of particular interest since strong interanalyte spectral interferences arise and regions with high and low signal intensity alternate in the spectra. Results show that multiple linear regression (MLR) on the wavelengths selected by SPA yields models with better prediction capabilities than principal component regression (PCR) and partial least squares (PLS) models. A standard genetic algorithm (GA) used for comparison yielded results similar to SPA for Mn, Cr and Fe, and better predictions for Mo and Ni. However, in all cases, the GA resulted in models less parsimonious than SPA. The average of the root mean square relative error of prediction (RMSREP) obtained for the five analytes was 1.4% for MLR–SPA, 1.0% for MLR–GA, 2.2% for PCR, and 2.1% for PLS. Since the computational time demanded by SPA grows with the square of the number of spectral variables, a pre-selection procedure based on the identification of emission peaks is proposed. This procedure decreased selection time by a factor of 20, without significantly degrading the results.

Modified microelectrodes and multivariate calibration for flow injection amperometric simultaneous determination of ascorbic acid, dopamine, epinephrine and dipyrone.

Flow injection amperometric quantification of ascorbic acid (AA), dopamine (DA), epinephrine (EP) and dipyrone (DI) in mixtures (in the microgram g-1 range) was successfully performed by using an array of microelectrodes with units modified by the electrodeposition of different noble metals, together with multivariate calibration analysis. The four groups of microelectrodes utilized included a pure gold electrode and electrodes modified by electrodeposition of platinum, palladium or a mixture of platinum + palladium. The array of microelectrodes was inserted in a flow cell and the amperometric data acquisition was performed with a four-channel potentiostat. The analysis of the resulting signals was carried out by a multivariate calibration method, using a group of 16 standard mixtures selected by a two-level factorial design. The analysis of synthetic samples and pharmaceutical compounds containing AA and DI led to very similar values to those obtained by the classical iodimetric analysis. The average absolute errors (in microgram g-1) calculated for each analyte were 0.3, 0.2, 0.4 and 0.4 for AA, DA, EP and DI, respectively.

Near infrared reflectance spectrometry classification of cigarettes using the successive projections algorithm for variable selection

This paper proposes a methodology for cigarette classification employing Near Infrared Reflectance spectrometry and variable selection. For this purpose, the Successive Projections Algorithm (SPA) is employed to choose an appropriate subset of wavenumbers for a Linear Discriminant Analysis (LDA) model. The proposed methodology is applied to a set of 210 cigarettes of four different brands. For comparison, Soft Independent Modelling of Class Analogy (SIMCA) is also employed for full-spectrum classification. The resulting SPA-LDA model successfully classified all test samples with respect to their brands using only two wavenumbers (5058 and 4903 cm(-1)). In contrast, the SIMCA models were not able to achieve 100% of classification accuracy, regardless of the significance level adopted for the F-test. The results obtained in this investigation suggest that the proposed methodology is a promising alternative for assessment of cigarette authenticity.

Digital image-based flame emission spectrometry

A digital image-based flame emission spectrometric (DIB-FES) method for the quantitative chemical analysis is proposed here for the first time. The DIB-FES method employs a webcam to capture the digital images which are associated to a radiation emitted by the analyte into an air-butane flame. Since the detection by webcam is based on the RGB (red-green-blue) colour system, a novel mathematical model was developed in order to build DIB-FES analytical curves and estimate figures of merit for the proposed method. In this approach, each image is retrieved in the three R, G and B individual components and their values were used to define a position vector in RGB three-dimensional space. The norm of this vector is then adopted as the RGB-based value (analytical response) and it has revealed to be linearly related to the analyte concentration. The feasibility of the DIB-FES method is illustrated in three applications involving the determination of lithium, sodium and calcium in anti-depressive drug, physiological serum and water, respectively. In comparison with the traditional flame emission spectrometry (trad-FES), no statistic difference has been observed between the results by applying the paired t-test at the 95% confidence level. However, the DIB-FES method has offered the largest sensitivities and precision, as well as the smallest limits of detection and quantification for the three analytes. These advantageous characteristics are attributed to the trivariate nature of the detection by webcam.

Classification of edible vegetable oils using square wave voltammetry with multivariate data analysis.

This paper proposes a simple and non-expensive electroanalytical methodology for classification of edible vegetable oils with respect to type (canola, sunflower, corn and soybean) and conservation state (expired and non-expired shelf life). The proposed methodology employs an alcoholic extraction procedure followed by square wave voltammetry (SWV). Two chemometric methods were compared for classification of the resulting voltammograms, namely Soft Independent Modelling of Class Analogy (SIMCA) and Linear Discriminant Analysis (LDA) with variable selection by the Successive Projections Algorithm (SPA). The results were evaluated in terms of errors in a set of samples not included in the modelling process. The best results were obtained with the SPA-LDA method, which correctly classified all samples in terms of type and conservation state.

Flow-batch technique for the simultaneous enzymatic determination of levodopa and carbidopa in pharmaceuticals using PLS and successive projections algorithm.

An enzymatic flow-batch system with spectrophotometric detection was developed for simultaneous determination of levodopa [(S)-2 amino-3-(3,4-dihydroxyphenyl)propionic acid] and carbidopa [(S)-3-(3,4-dihydroxyphenyl)-2-hydrazino-2-methylpropionic acid] in pharmaceutical preparations. The data were analysed by univariate method, partial least squares (PLS) and a novel variable selection for multiple lineal regression (MLR), the successive projections algorithm (SPA). The enzyme polyphenol oxidase (PPO; EC 1.14.18.1) obtained from Ipomoea batatas (L.) Lam. was used to oxidize both analytes to their respective dopaquinones, which presented a strong absorption between 295 and 540 nm. The statistical parameters (RMSE and correlation coefficient) calculated after the PLS in the spectral region between 295 and 540 nm and MLR-SPA application were appropriate for levodopa and carbidopa. A comparative study of univariate, PLS, in different ranges, and MLR-SPA chemometrics models, was carried out by applying the elliptical joint confidence region (EJCR) test. The results were satisfactory for PLS in the spectral region between 295 and 540 nm and for MLR-SPA. Tablets of commercial samples were analysed and the results obtained are in close agreement with both, spectrophotometric and HPLC pharmacopeia methods. The sample throughput was 18 h(-1).