Variable reduction algorithm for atomic emission spectra: application to multivariate calibration and quantitative analysis of industrial samples

Griffiths, Michael L.; Svozil, Daniel; Worsfold, Paul J.; Denham, Susan; Evans, E. Hywel

doi:10.1039/b203239m

Cited by 16 publications

(11 citation statements)

References 36 publications

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“…m), reduced prediction errors are common when care is taken to select wavelengths spanning useful analyte predictive information. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] However, this prediction error reduction comes with a tradeoff of potential prediction variance inflation. 15,18,22,24,25 The methods of RR, PLS, or PCR can be used when wavelengths are selected such that n !…”

Section: Introductionmentioning

confidence: 99%

“…13,21,23 Wavelength selection algorithms such as genetic algorithms or simulated annealing commonly necessitate lengthy iterative sequential processes involving wavelength selection, model forming using RR, PLS, or another method, and prediction testing of the selected wavelengths. 6,[14][15][16] These and other optimization algorithms often require user-set operating parameters. Altering these parameters for a specific algorithm can result in different subsets of wavelengths being selected and, hence, the dilemma of selecting wavelengths with chance correlations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization

2010

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Tikhonov regularization (TR) is a general method that can be used to form a multivariate calibration model and numerous variants of it exist, including ridge regression (RR). This paper reports on the unique flexibility of TR to form a model using full wavelengths (RR), individually selected wavelengths, or multiple bands of selected wavelengths. Of these three TR variants, the one based on selection of wavelength bands is found to produce lower prediction errors. As with most wavelength selection algorithms, the model vector magnitude indicates that this error reduction comes with a potential increase in prediction uncertainty. Results are presented for near-infrared, ultraviolet-visible, and synthetic spectral data sets. While the focus of this paper is wavelength selection, the TR methods are generic and applicable to other variable-selection situations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization

2010

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“…In a following work, Griffiths et al 74 studied how to reduce the ICP-AES (segmented-array charge-coupled device detector) raw variables (5684 wavelenghts per spectrum). This application holds many similarities with classical molecular spectrometry from where they selected two advanced algorithms, applied in three steps: (i) application of an uninformative variable elimination PLSR algorithm (UVE-PLSR), which identifies variables with close-to-zero regression coefficients; (ii) application of an informative variable degradation-PLSR, which ranked variables using a ratio calculated as the regression coefficient divided by its estimated standard error; and (iii) selection of the variables according to that ratio.…”

Section: Inductively Coupled Plasmamentioning

confidence: 99%

A tutorial on multivariate calibration in atomic spectrometry techniques

Cal-Prieto

Gómez-Carracedo

Carlosena

et al. 2008

J. Anal. At. Spectrom.

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Coupling multivariate regression methods to atomic spectrometry is an emerging field from which important advantages can be obtained. These include lower workloads, increased laboratory turnarounds, economy, higher efficiency in method development, and relatively simple ways to take account of complex interferences. In this paper four typical regression methods (ordinary multiple linear regression, principal components regression, partial least squares and artificial neural networks) are presented in a practice-oriented way. The main emphasis is placed on explaining their advantages, drawbacks, how to solve the latter and how atomic spectrometry can benefit from multivariate regression. Finally, a retrospective review considering the last sixteen years is made to present practical applications on: flame-, hydride generation-, electrothermalatomic absorption spectrometry; inductively coupled plasma spectrometry and laser-induced breakdown spectrometry.

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“…Common methods for accomplishing wavelength selection are forward selection, stepwise regression (SWR), genetic algorithms, simulated annealing, etc. [3][4][5][6] Such methods often require arbitrary user-set optimization parameters. Altering these complicated parameters for a specific algorithm leads to different wavelength subsets.…”

Section: Introductionmentioning

confidence: 99%

“…[7][8][9] The greater the ratio of the number of wavelengths to the number of samples, the greater the prospect of the dilemma occurring. 10 Additionally, many wavelength selection algorithms [3][4][5][6] only use prediction bias information in selecting wavelengths, i.e., sequential variation of wavelength subsets followed by model determination using PCR, RR, PLS, MLR, etc., and then computation of an accuracy (bias) diagnostic for model comparisons and final selection of the wavelength subset. Optimization of such a criterion based on only using calibration data, e.g., root mean square of calibration (RMSEC), results in over-fitting and poor predictions for a new X.…”

Section: Introductionmentioning

confidence: 99%

Wavelength Selection for Multivariate Calibration Using Tikhonov Regularization

2007

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Prediction of sample properties using spectroscopic data with multivariate calibration is often enhanced by wavelength selection. This paper reports on a built-in wavelength selection method in which the estimated regression vector contains zero to near-zero coefficients for undesirable wavelengths. The method is based on Tikhonov regularization with the model 1-norm (TR1) and is applied to simulated and near-infrared (NIR) spectral data. Models are also formed from wavelength subsets determined by the standard method of stepwise regression (SWR). Harmonious (bias/variance tradeoff) and parsimonious considerations are compared with and without wavelength selection for principal component regression (PCR), ridge regression (RR), partial least squares (PLS), and multiple linear regression (MLR). Results show that TR1 models generally contain large baseline regions of near-zero coefficients, thereby essentially achieving built-in wavelength selection. For example, wavelengths with spectral interferences and/or poor signal-to-noise ratios obtain near zero regression coefficients. Results often improve with TR1 models, compared to full wavelength PCR, RR, and PLS models. The SWR subset results are similar to those for the TR1 models using the NIR data and worse with the simulated spectral situations. In general, wavelength selection improves prediction accuracy at a sacrifice to a potential increase in variance and the parsimony remains nearly equivalent compared to full wavelength models. New insights gained from the reported studies provide useful guidelines on when to use full wavelengths or use wavelength selection methods. Specifically, when a small number of large wavelength effects (good sensitivity and selectivity) exist, subset selection by SWR (with caution) and TR1 do well. With a small to moderate number of large to moderate sized wavelength effects, TR1 is better. Lastly, when a large number of small effects are present, full wavelengths with the methods of PCR, RR, or PLS are best.

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Variable reduction algorithm for atomic emission spectra: application to multivariate calibration and quantitative analysis of industrial samples

Cited by 16 publications

References 36 publications

Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization

Spectral Multivariate Calibration with Wavelength Selection Using Variants of Tikhonov Regularization

A tutorial on multivariate calibration in atomic spectrometry techniques

Wavelength Selection for Multivariate Calibration Using Tikhonov Regularization

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