Selection In Multivariate Calibration Research Articles

Spectral variables selection in multivariate calibration of concentrations of C, Mn, Si, Cr, Ni and Cu in low-allow steels by laser induced breakdown spectroscopy

Multivariate calibrations of concentrations of C, Mn, Si, Cr, Ni and Cu have been developed by the partial least squares method for 31 to 39 standard samples of low-alloy steels using low-resolution emission spectra (190-440 nm, resolution 0.4 nm, step 0.1 nm). Three methods of spectral variables selection are considered: a method of ranking spectral variables by their correlation coefficient with the value of the calibrated parameter, a successive projection algorithm and an original modification of searching combination moving windows. The partial least squares model with the spectral variables selection by the method of the searching combination moving windows for C is quantitative: the root mean square error is 0.004%, the residual predictive deviation in the test dataset is 23.4 in the concentration range 0.13 to 0.43%. Calibrations of Mn (0.04% and 5.2 in the range of 0.47-1.15%), Si (0.003% and 20.7 in the range of 0.15-0.33%), Cr (0.04% and 3.1 in the range of 0.09-0.43%) and Ni (0.01% and 4.8 in the range of 0.05-0.25%) are also quantitative. For Cu in the concentration range of 0.06-0.26%, calibration is qualitative (0.04% and 1.4). Keywords: laser induced breakdown spectroscopy, multivariate calibration, partial least squares, low-alloy steels

Adaptive Variable Re-weighting and Shrinking Approach for Variable Selection in Multivariate Calibration for Near-infrared Spectroscopy

Abstract With the generation of high-dimensional data from spectroscopic instruments, the role of variable selection in spectral modeling has become very important. This research proposes a new variable selection algorithm, named adaptive variable re-weighting and shrinking approach (AVRSA), based on model population analysis (MPA) and weighted bootstrap sampling (WBS). In this algorithm, WBS is used to generate sub-datasets for modeling in each iteration round, and the variable weight and space are updated by statistically evaluating the optimal sub-models. Unlike most other variable selection methods, the average prediction performance of the optimal sub-models by AVRSA must be preferable to that of the previous iteration. The best informative variables are obtained until no further optimal sub-models are generated. This method is checked on three near infrared (NIR) datasets. Three variable selection methods, including competitive adaptive reweighted sampling (CARS), MonteCarlo uninformative variable elimination (MC-UVE) and iteratively variable subset optimization (IVSO), are used for comparison. Compared with these variable selection algorithms, AVRSA selects the least informative variables, which is convenient for the development of portable instruments. Compared with the full-spectrum PLS model, the root mean square error of the validation set (RMSEP) of corn starch is decreased from 0.2614 to 0.1093, and the RMSEP of corn protein is decreased from 0.0977 to 0.0374. In addition, the RMSEP of the wheat dataset is decreased from 0.2585 to 0.2157, and the RMSEP of the wheat kernel dataset is decreased from 0.7816 to 0.6661. The results show that the proposed method is very efficient for the high-dimensional spectrum to find the best variables and improve the model's prediction performance.

A novel hybrid feature selection strategy in quantitative analysis of laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) has been recognized as a significant tool for quantitative analysis of elements with its unique advantages, especially in combination with multivariate calibration methods. However, LIBS spectra typically include large amounts of high-dimensional data that affect the predictive accuracy of multivariate calibration based on LIBS. Feature selection, as an important preprocessing step in data mining, can improve the performance of the multivariate calibration model by eliminating the redundant and irrelevant features. In this study, a hybrid feature selection method based on V-WSP-PSO was proposed to improve the accuracy of LIBS analysis. The proposed method combines the advantages of V-WSP based filter method and particle swarm optimization (PSO) based wrapper method. The uncorrelated and redundant features were first eliminated by V-WSP method to form a simplified input subset, and then the retained features were further refined by PSO method to find a small set of features with high predictive accuracy. In order to evaluate the performance of proposed method, LIBS experiments were performed using 28 coal samples, and a nonlinear multivariate calibration method based on kernel extreme learning machine (KELM) was selected to implement the proposed hybrid feature selection method for calorific value determination of coal. Comparing the proposed method with several other feature selection methods shows that the V-WSP-PSO method is best in terms of number of selected features and predictive accuracy. Finally, 114 features were selected from full spectrum (27620 features) by V-WSP-PSO method and the best root mean square error of cross validation (RMSECV) and determination coefficient of cross validation (RCV2) were 0.4013 MJ/kg and 0.9908, root mean square error of prediction (RMSEP) and determination coefficient of prediction (RP2) were 0.3534 MJ/kg and 0.9894. The overall results demonstrate that the V-WSP-PSO method is more efficient to reduce the redundant features, calculation time and improve the model performance, and it is a good alternative for feature selection in multivariate calibration.

Epistasis-based FSA: Two versions of a novel approach for variable selection in multivariate calibration

Variable Selection in large datasets is a commonly procedure in multivariate calibration, which is a field of study from chemometrics. Selecting the most informative variables becomes an important step to build mathematical models through statistical techniques in order to predict some property of interest from an analyzed sample. Recombination-based search methods such as Genetic Algorithms (GAs) have been widely used as variable selection techniques to solve several optimization problems. However, previous works from literature have emphasized the schemata disruption problem caused by genetic operators. Therefore, this paper proposes two versions of an epistasis-based implementation (EbFSA) as a novel approach for variable selection in multivariate calibration problems, where each version is deterministic and performs a different strategy. The use of epistasis concepts becomes important to assess the genes (variables) interdependence. Based on our experimental results, we are able to claim EbFSA can select the most informative variables and overcome some state-of-the-art algorithms.

A variable informative criterion based on weighted voting strategy combined with LASSO for variable selection in multivariate calibration

High-throughput spectra data with large number of variables (wavelength) will make the prediction of multivariate calibration model unreliable, in which case, the sparse statistical methods such as least absolute shrinkage and selection operator (LASSO) are gradually being valued by researchers. In this study, a novel variable informative criterion based on weighted voting strategy combined with least absolute shrinkage and selection operator (WV-LASSO) has been proposed. Monte Carlo Sampling (MCS) is used for generating a large number of sub-models. In each Monte Carlo circulation, the regression coefficients and variable selection information of LASSO model will be recorded. In the present work, weighted voting strategy based on regression coefficients information combined with selected variable frequency of all sub-models is used for evaluating the importance of variable. Different from specific methods, variable informative (importance) criterion can be more extensive and flexible for algorithm design. Then an approach called exponentially decreasing function (EDF) is applied to create a variable selection method with WV-LASSO. The performance of this method was evaluated by three near-infrared (NIR) datasets. Compared with some efficient variable selection methods based on different informative criterions including variable importance projection (VIP), Monte Carlo uninformative variable elimination (MC-UVE), randomization test (RT), competitive adaptive reweighted sampling (CARS), stability competitive adaptive reweighted sampling (SCARS), variable iterative space shrinkage approach (VISSA), interval variable iterative space shrinkage approach (iVISSA), LASSO coupled with sampling error profile analysis (SEPA-LASSO) and variable combination population analysis (VCPA), and so forth, the variable selection method proposed in this paper shows better prediction and interpretation ability and has potential for constructing various variable selection methods by combining other selection strategies.

Variable selection in multivariate calibration based on clustering of variable concept

Recently we have proposed a new variable selection algorithm, based on clustering of variable concept (CLoVA) in classification problem. With the same idea, this new concept has been applied to a regression problem and then the obtained results have been compared with conventional variable selection strategies for PLS. The basic idea behind the clustering of variable is that, the instrument channels are clustered into different clusters via clustering algorithms. Then, the spectral data of each cluster are subjected to PLS regression. Different real data sets (Cargill corn, Biscuit dough, ACE QSAR, Soy, and Tablet) have been used to evaluate the influence of the clustering of variables on the prediction performances of PLS. Almost in the all cases, the statistical parameter especially in prediction error shows the superiority of CLoVA-PLS respect to other variable selection strategies. Finally the synergy clustering of variable (sCLoVA-PLS), which is used the combination of cluster, has been proposed as an efficient and modification of CLoVA algorithm. The obtained statistical parameter indicates that variable clustering can split useful part from redundant ones, and then based on informative cluster; stable model can be reached.

Multi-objective Genetic Algorithm for Variable Selection in Multivariate Classification Problems: A Case Study in Verification of Biodiesel Adulteration

This paper proposes multi-objective genetic algorithm for the problem of variable selection in multivariate calibration. We consider the problem related to the classification of biodiesel samples to detect adulteration, Linear Discriminant Analysis classifier. The goal of the multi--objective algorithm is to reduce the dimensionality of the original set of variables; thus, the classification model can be less sensitive, providing a better generalization capacity. In particular, in this paper we adopted a version of the Non-dominated Sorting Genetic Algorithm (NSGA-II) and compare it to a mono-objective Genetic Algorithm (GA) in terms of sensitivity in the presence of noise. Results show that the mono-objective selects 20 variables on average and presents an error rate of 14%. One the other hand, the multi-objective selects 7 variables and has an error rate of 11%. Consequently, we show that the multi-objective formulation provides classification models with lower sensitivity to the instrumental noise when compared to the mono-objetive formulation

Using variable combination population analysis for variable selection in multivariate calibration

Variable (wavelength or feature) selection techniques have become a critical step for the analysis of datasets with high number of variables and relatively few samples. In this study, a novel variable selection strategy, variable combination population analysis (VCPA), was proposed. This strategy consists of two crucial procedures. First, the exponentially decreasing function (EDF), which is the simple and effective principle of ‘survival of the fittest’ from Darwin’s natural evolution theory, is employed to determine the number of variables to keep and continuously shrink the variable space. Second, in each EDF run, binary matrix sampling (BMS) strategy that gives each variable the same chance to be selected and generates different variable combinations, is used to produce a population of subsets to construct a population of sub-models. Then, model population analysis (MPA) is employed to find the variable subsets with the lower root mean squares error of cross validation (RMSECV). The frequency of each variable appearing in the best 10% sub-models is computed. The higher the frequency is, the more important the variable is. The performance of the proposed procedure was investigated using three real NIR datasets. The results indicate that VCPA is a good variable selection strategy when compared with four high performing variable selection methods: genetic algorithm–partial least squares (GA–PLS), Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS), competitive adaptive reweighted sampling (CARS) and iteratively retains informative variables (IRIV). The MATLAB source code of VCPA is available for academic research on the website: http://www.mathworks.com/matlabcentral/fileexchange/authors/498750.

Enhanced genetic operators design for waveband selection in multivariate calibration based on NIR spectroscopy

Nowadays, the techniques employed in data acquisition provide huge amounts of data. Some parts of the information are related to the others, making dimensionality reduction desirable, and losing less information as much as possible, in order to decrease computational times and complexity when applying any ensuing data mining technique. Genetic algorithms offer the possibility of selecting which variables contain the most relevant information to represent all the original ones. The traditional genetic operators seem to be too general, leading to results that could be improved by means of designed genetic operators that employ some available problem‐specific information. Especially, when dealing with calibration by means of near‐infrared spectral data, which use to contain thousands of variables, it is known that not isolated wavelengths but wavebands allow a more robust model design. This aspect should be taken into account when crossing individuals. We propose three crossover operators specifically designed for calibration with near‐infrared spectral data, based on a pseudo‐random two‐point crossover, where the first point is chosen randomly, and the selection of the second point is guided by problem‐specific information. We compare their performance with that of state‐of‐the‐art operators. We combine these new genetic algorithm‐based variable selection designs with partial least squares regression and fuzzy systems based calibration.Our benchmark consists of two real‐world high‐dimensional data sets, corresponding to polyetheracrylat, where hydroxyl number, viscosity, and acidity are on‐line monitored; and melamine resin production, where the chilling point (CP) is considered in order to regulate the condensation. We show that designed operators promote wavebands selection, achieve better‐quality solutions, and converge faster and smoother than state‐of‐the‐art operators. Copyright © 2014 John Wiley & Sons, Ltd.

A simple idea on applying large regression coefficient to improve the genetic algorithm-PLS for variable selection in multivariate calibration

Genetic algorithm-based couple with partial least squares (PLS) has been successfully applied for variable selection in multivariate calibration. On the basis of the fact that a large PLS regression coefficient indicates an important variable, a new and simple idea that the structure of a proportion of chromosomes in the initial population is determined by the large regression coefficient is presented in this study. The regression coefficient is obtained by establishing the PLS modeling on the autoscaled data. With this improved approach, the modified GA-PLS method not only makes the optimization better toward the optimal solution, but also obeys the rule of the GAs. The results obtained through investigating one simulated dataset and two near infrared dataset show that the modified method has made much improvement on variable selection compared to the original GA-PLS.

Weighted Fusion of Multiple Models for Wavelength Selection

A new method based on the weighted fusion of multiple models is presented for wavelength selection in multivariate calibration of spectral data. It fuses the regression coefficients of multiple models with weights based on minimum mean square error to improve the accuracy and stability of the wavelength selection. To validate the performance of the proposed method, it was applied to the partial least squares (PLS) modeling of three near-infrared spectral datasets and compared with full-spectrum PLS, genetic algorithm-based PLS, and uninformative variable elimination-based PLS methods. Results show that the proposed method can effectively select the informative wavelength and enhance the prediction ability of the PLS model. On account of its simpler algorithm and higher efficiency, it can be widely used in practical applications.

A Flow System for Generation of Concentration Perturbation in Two-Dimensional Correlation Near-Infrared Spectroscopy: Application to Variable Selection in Multivariate Calibration

A flow system is proposed to produce a concentration perturbation in liquid samples, aiming at the generation of two-dimensional correlation near-infrared spectra. The system presents advantages in relation to batch systems employed for the same purpose: the experiments are accomplished in a closed system; application of perturbation is rapid and easy; and the experiments can be carried out with micro-scale volumes. The perturbation system has been evaluated in the investigation and selection of relevant variables for multivariate calibration models for the determination of quality parameters of gasoline, including ethanol content, MON (motor octane number), and RON (research octane number). The main advantage of this variable selection approach is the direct association between spectral features and chemical composition, allowing easy interpretation of the regression models.

Combination of Ant Colony Optimization with Various Local Search Strategies. A Novel Method for Variable Selection in Multivariate Calibration and QSPR Study

AbstractRecently, we applied successfully ant colony optimization (ACO) to wavelength selection problem. In this paper ant colony system (ACS), a version of ACO algorithms, has been applied to variable selection in multivariate calibration and QSPR studies. In addition, the effect of combination of ACS algorithm with various local search strategies was inspected. The suggested local search strategies included forward selection, backward elimination, forward selection together with backward elimination, backward elimination together with forward selection, genetic algorithm, and tabu search. Parameters of ACS and combined local search strategy were optimized. The results obtained from all ACS algorithms indicated that combination of various local search strategies to the ACS algorithm improved the performance of the ACS algorithm.

An Improved Ensemble Method for Completely Automatic Optimization of Spectral Interval Selection in Multivariate Calibration

In our recent work, Monte Carlo Cross Validation Stacked Regression (MCCVSR) is proposed to achieve automatic optimization of spectral interval selection in multivariate calibration. Though MCCVSR performs well in normal conditions, it is still necessary to improve it for more general applications. According to the well-known principle of “garbage in, garbage out (GIGO)”, as a precise ensemble method, MCCVSR might be influenced by outlying and very bad submodels. In this paper, a statistical test is designed to exclude the ruinous submodels from the ensemble learning process, therefore, the combination process becomes more reliable. Though completely automated, the proposed method is adjustable according to the nature of the data analyzed, including the size of training samples, resolution of spectra and quantitative potentials of the submodels. The effectiveness of the submodel refining is demonstrated by the investigation of a real standard data.

An ensemble of Monte Carlo uninformative variable elimination for wavelength selection

An improved method based on an ensemble of Monte Carlo uninformative variable elimination (EMCUVE) is presented for wavelength selection in multivariate calibration of spectral data. The proposed algorithm introduces Monte Carlo (MC) strategy to uninformative variable elimination-PLS (UVE-PLS) instead of leave-one-out strategy for estimating the contributions of each wavelength variable in the PLS model. In EMCUVE wavelength variables are evaluated by different Monte Carlo uninformative variable elimination (MCUVE) models. Moreover, a fusion of MCUVE and the vote rule can obtain an improvement over the original uninformative variable elimination method. Results obtained from simulated data and real data sets demonstrate that EMCUVE can properly carry out wavelength selection in the course of data analysis and improve predictive ability for multivariate calibration model.

MCCV stacked regression for model combination and fast spectral interval selection in multivariate calibration

The present paper deals with variable selection in multivariate calibration of spectral data. A machine learning method, stacked regression is improved and then used to linearly combine different regression models built on sequential spectral intervals. While automatically extracting the spectral intervals carrying useful information for quantitative analysis, the proposed method can achieve a combined regression model with minimum RMSEMCCV (root mean squared error of Monte Carlo cross validation) among all possible linear combinations of the interval models under certain reasonable constraints. As expected, this method demonstrates considerable immunity against overfitting yet holds good prediction property. Due to some inherent characteristics of stacked regression, the method is economical to compute and the computation time is acceptable for large data sets. Two real spectral data sets are investigated by this method and the results are compared with those obtained by simple interval PLS.

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

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.

Variable Selection in Multivariate Calibration of a Spectroscopic Glucose Sensor

A variable selection method that reduces prediction bias in partial least-squares regression models was developed and applied to near-infrared absorbance spectra of glucose in pH buffer and cell culture medium. Comparisons between calibration and prediction capability for full spectra and reduced sets were completed. Variable selection resulted in statistically equivalent errors while reducing the number of wavelengths needed to fit the calibration data and predict concentrations from new spectra. Fewer than 25 wavelengths were selected to produce errors statistically equivalent to those yielded by the full set containing over 500 wavelengths. The algorithm correctly chose the glucose absorption peak areas as the information-carrying spectral regions.

Genetic algorithms as a method for variable selection in multiple linear regression and partial least squares regression, with applications to pyrolysis mass spectrometry

Four optimising methods for variable selection in multivariate calibration have been described: one for determining the optimal subset of variables to give the best possible root-mean-square error of prediction (RMSEP) in a multiple linear regression (MLR) model, the second for determining the optimal subset of variables which produce a model with RMSEP less than or equal to a given value. Algorithms three and four were identical to algorithms one and two, respectively, except that this time they use a cost function derived from a partial least squares (PLS) model rather than an MLR model. Applied to a typical set of pyrolysis mass spectrometry data the first variable selection method is shown to reduce the RMSEP of the optimal MLR or PLS model significantly when the number of variables is decreased by approximately half. Alternatively, the number of variables may be reduced substantially (> 10-fold) with no loss in RMSEP.

Genetic Algorithms as a Tool for Wavelength Selection in Multivariate Calibration

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTGenetic Algorithms as a Tool for Wavelength Selection in Multivariate CalibrationDelphine. Jouan-Rimbaud, Desire-Luc. Massart, Riccardo. Leardi, and Onno E. De NoordCite this: Anal. Chem. 1995, 67, 23, 4295–4301Publication Date (Print):December 1, 1995Publication History Published online1 May 2002Published inissue 1 December 1995https://doi.org/10.1021/ac00119a015RIGHTS & PERMISSIONSArticle Views686Altmetric-Citations250LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (732 KB) Get e-Alerts Get e-Alerts