A theoretical foundation for the PLS algorithm

Lorber, Avraham; Wangen, L.E.; Kowalski, Bruce R.

doi:10.1002/cem.1180010105

Cited by 437 publications

(174 citation statements)

References 7 publications

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“…In PLSR, the original Xdata, are projected onto latent variables on which the regressions are performed. Further details about PLSR are given elsewhere [25][26][27]. Principal component analysis (PCA) was used to get a general overview over the structure in the data.…”

Section: Calculations and Error Estimatesmentioning

confidence: 99%

The prediction of fatty acid structure from selected ions in electron impact mass spectra of fatty acid methyl esters

Mjøs¹

2004

Euro J Lipid Sci & Tech

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The prediction of fatty acid structure from selected ions in electron impact mass spectra of fatty acid methyl estersThe possibility of fatty acid identification from ions in the mass region of 50-110 amu in electron impact mass spectra has been studied by application of various multivariate techniques. The focus has mainly been on the prediction of the number of double bonds in methylene-interrupted polyunsaturated fatty acids isolated from marine lipids.The number of double bonds in these fatty acids could be predicted with high accuracy, both by partial least squares regression on all ions in this region, and by multiple linear regressions on selected subsets of 5-6 ions. The subsets with optimal predictive power have been found, and the ability to distinguish between methylene interrupted polyunsaturated fatty acids and other fatty acids have also been evaluated.

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Section: Calculations and Error Estimatesmentioning

confidence: 99%

The prediction of fatty acid structure from selected ions in electron impact mass spectra of fatty acid methyl esters

Mjøs¹

2004

Euro J Lipid Sci & Tech

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“…Multivariate calibration methods are well-known to play a very important role in the multicomponent analyses. [3][4][5][6] Partial least squares (PLS) regression as a full spectrum multivariate calibration method was originally developed by Wold 7 and chemically applied by Wold et al 8,9 It has been successfully applied to the quantitative analyses of spectroscopic 10,11 as well as electrochemical data. 12 The PLS methods are represented by two modifications, known as PLS-1 and PLS-2.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Determination of Phenol and Mononitrophenol Isomers Using PLS Regression and Conventional and Derivative Spectrophotometry

et al. 2005

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Summary -The partial least squares regression method (PLS) was tested as a calibration procedure for the simultaneous determination of phenol, o-nitrophenol, m-nitrophenol and p-nitrophenol by both conventional and first derivative UV/Vis spectrophotometry. The experiments were conducted in the acidic, neutral and basic media. The results obtained by the application of the PLS procedure on the conventional and first derivative spectra in two solvent media were compared. It was found that the results obtained in the basic medium have better performance characteristics than those obtained in the acidic or neutral media. Comparable results were obtained in the case of both conventional and first derivative absorbance data. The proposed method was applied to the determination of the four phenol derivatives in natural spiked water samples at concentration levels between 1.0 and 10.0 µg ml -1 with average recoveries in the range 96% -99%.

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“…The NIR reflectance spectra of these solutions were measured from 1100 to 1700 nm. The PLS calibration model was constructed using these eight calibration mixtures in the range of 1100 to 1700 nm using three latent variables and MATLAB code written inhouse using the algorithm of Lorder et al 47 The resulting PLS calibration model was used to estimate the solid profiles shown in Figure 6 for comparison to the model estimated mass profiles. It should be emphasized that the reflectance R was used in the PLS calibration rather than the conventional quantity log(1/R), as the raw signal R gave the best linearity with the fewest number of factors.…”

Section: ■ Experimental Sectionmentioning

confidence: 99%

Kinetic Modeling of Dissolution and Crystallization of Slurries with Attenuated Total Reflectance UV–Visible Absorbance and Near-Infrared Reflectance Measurements

et al. 2013

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Slurries are often used in chemical and pharmaceutical manufacturing processes but present challenging online measurement and monitoring problems. In this paper, a novel multivariate kinetic modeling application is described that provides calibration-free estimates of timeresolved profiles of the solid and dissolved fractions of a substance in a model slurry system. The kinetic model of this system achieved data fusion of time-resolved spectroscopic measurements from two different kinds of fiber-optic probes. Attenuated total reflectance UV−vis (ATR UV−vis) and diffuse reflectance near-infrared (NIR) spectra were measured simultaneously in a small-scale semibatch reactor. A simplified comprehensive kinetic model was then fitted to the time-resolved spectroscopic data to determine the kinetics of crystallization and the kinetics of dissolution for online monitoring and quality control purposes. The parameters estimated in the model included dissolution and crystal growth rate constants, as well as the dissolution rate order. The model accurately estimated the degree of supersaturation as a function of time during conditions when crystallization took place and accurately estimated the degree of undersaturation during conditions when dissolution took place. S ignificant progress in the area of multivariate batch process monitoring, modeling, and control has been made over the last 2 decades; 1 however, strategies for monitoring and modeling of slurries have not been widely reported, despite the fact that slurries are often used in chemical and pharmaceutical manufacturing processes. Many of the early developments in process analysis can be attributed to groundbreaking work of Nomikos and MacGregor 2,3 and Wold and co-workers.4−6 These efforts were largely focused on the use of principal component analysis (PCA) and partial least-squares (PLS) to develop multivariate statistical process control (MSPC) models for characterization of process operating conditions and thereafter the definition of normal operating conditions for the production of batches fulfilling the desired specifications.1 These models were then used to monitor future batches, product quality, and yield, as well as detect faults and diagnose process deviations.An alternative to this approach called multivariate kinetic modeling has also seen significant development over the last 2 decades. In these approaches, first-principles physical models are fitted directly to multivariate spectroscopic measurements where, typically, the adjustable model parameters are rate constants.7−10 Recently, kinetic model fitting methods were extended to achieve fusion of calorimetric measurements of univariate nature with multivariate spectroscopic measurements, 11−14 extended to incorporate chemical equilibria, 15,16 used for estimation of additional parameters such as activation energies and reaction enthalpies, 17,18 and for fitting of extents of reaction in gas−liquid systems. 19 These modeling approaches offer some advantages and some drawbacks compared to...

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A theoretical foundation for the PLS algorithm

Cited by 437 publications

References 7 publications

The prediction of fatty acid structure from selected ions in electron impact mass spectra of fatty acid methyl esters

The prediction of fatty acid structure from selected ions in electron impact mass spectra of fatty acid methyl esters

Simultaneous Determination of Phenol and Mononitrophenol Isomers Using PLS Regression and Conventional and Derivative Spectrophotometry

Kinetic Modeling of Dissolution and Crystallization of Slurries with Attenuated Total Reflectance UV–Visible Absorbance and Near-Infrared Reflectance Measurements

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