Self-modelling curve resolution in studies of spectrometric titrations of multi-equilibria systems by factor analysis

Tauler, Romà; Casassas, E.; Izquierdo‐Ridorsa, A.

doi:10.1016/s0003-2670(00)84662-0

Cited by 65 publications

(46 citation statements)

References 17 publications

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“…The outline of the xacto blade is clearly sharper in the short-wavelength image than in the long-wavelength image. In addition, Figure 3C shows a profile of the transmission intensity across row 15 for pixels in columns 22 through 34 that span the transition across the [6][7] edge of the xacto blade. Clearly the transition is significantly sharper for the short-wavelength, demonstrating the dramatic effects of chromatic aberration.…”

Section: Resultsmentioning

confidence: 99%

“…n n = (ETE)-lETA m E+A (7) The process can be generalized further to augment the column dimension of C with selected calibration concentration residuals obtained from the predicted calibration reference values (see Eq. (8)) after CLS calibration and prediction or cross-validated prediction on the calibration samples or true prediction on a set of validation samples.…”

Section: E a = T P + Ementioning

confidence: 99%

“…[6] The concept of the PACLS algorithm was then hrther extended to a whole family of generalized multivariate augmented classical least squares (ACLS) methods. [7] Among these algorithms are the concentration-residual augmented CLS (CRACLS) algorithm, [8] spectralresidual augmented CLS (SRACLS), and the scores augmented CLS (SACLS) algorithm. The new augmented methods and the hybrid algorithm have been the subject of two patent applications[9, 101 and two provisional patent applications.…”

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confidence: 99%

“…A portion of this Appendix along with a demonstration of the SRACLS algorithm to rapidly update the calibration when different spectrometers are used in the collection of the unknown samples is presented in a paper that has recently been accepted for publication in Vibrational Spectroscopy. [7] Appendix B of this report documents the hyperspectral infrared analysis of ink jet printer inks using end-member analysis from commercial software and compares these commercial software results to those obtained from the use of the PACLS algorithm. The PACLS algorithm is shown in Appendix B to be able to correct the quantitative analysis of the ink image spectra for the presence of chromatic aberration in the data.…”

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confidence: 99%

“…If PLS or PCR are used, then concentration residuals must be included in the calibration process, and the method becomes one of the hybrid method described in SD6256. [7] The factor analysis can use either an orthogonal factor analysis method or any non-orthogonal factor analysis method. Once the factor analysis is completed, the scores, T, or the loadings, P, can be used to improve the CLS calibration model.…”

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confidence: 99%

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Improved Materials Aging Diagnostics and Mechanisms through 2D Hyperspectral Imaging Methods and Algorithms

Haaland¹,

Wehlburg²,

Martin³

et al. 2002

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The availability of new commercial hyperspectral imaging infrared spectrometers makes possible the quantitative analysis of materials without the need for standards. In the course of achieving this goal, we have developed a new family of augmented classical least-squares (ACLS) algorithms that have important improvements over other quantitative multivariate calibration methods. The new ACLS methods are described and their application to hyperspectral image analysis is presented. Demonstration is given for the use of ACLS methods to improve the quantitative analysis of hyperspectral image data when chromatic aberrations are present in the system. A comparison of several multivariate curve resolution methods to estimate purecomponent spectra without standards is presented. Finally, improvements to the multivariate curve resolution methods used to perform quantitative spectral analysis without standards are also presented. This report is a compilation of unpublished works describing these methods. Along with reference published and accepted journal papers, this body of work demonstrates the successful completion of the goals of this project. INTRODUCTIONIn this three-year research project, we set out to develop new methods of analysis of twodimensional hyperspectral Fourier transform infrared (FT-IR) images collected from a new generation of commercial FT-IR imaging spectrometers. The goal was to develop and apply new hyperspectral image analysis methods to the investigation of the aging of polymeric materials. We have accomplished this goal and have developed a whole new family of multivariate calibration methods that significantly improve the qualitative and quantitative analysis of spectral data whether the data are from hyperspectral images or from other sources. This report is a compilation of appendices from journal preprints, a patent specification, and another report that were all generated in part or in whole from this Laboratory Directed Research and Development (LDRD) project. Patent applications, published journal papers, and submitted journal papers related to this project are referenced but not included in this report.Because hyperspectral image data were not available at the beginning of this project, we initiated the development of a new classical least squares/ partial least squares (CLSPLS) hybrid multivariate analysis algorithm that was to create the basis of our hyperspectral image analyses. This hybrid algorithm was developed and programmed into several software codes. Celeste Drewien documented the implementation of the CLS/PLS hybrid algorithm for parallel processing computers.[l] The theory of the hybrid algorithm and an application to updating multivariate calibration models for the presence of unmodeled sources of near-infrared spectral variation in dilute aqueous solutions has also been published. [2] In the course of developing the hybrid algorithm, a significant improvement to the original CLS multivariate analysis algorithm[3-51 was developed. The improvement was called pre...

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Section: Resultsmentioning

confidence: 99%

Section: E a = T P + Ementioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Improved Materials Aging Diagnostics and Mechanisms through 2D Hyperspectral Imaging Methods and Algorithms

Haaland¹,

Wehlburg²,

Martin³

et al. 2002

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Selectivity, local rank, three‐way data analysis and ambiguity in multivariate curve resolution

Tauler

Smilde

Kowalski

1995

Journal of Chemometrics

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907

691

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SUMMARYA new multivariate curve resolution method is presented and tested with data of various levels of complexity. Rotational and intensity ambiguities and the effect of selectivity on resolution are the focus. Analysis of simulated data provides the general guidelines concerning the conditions for uniqueness of a solution for a given problem. Multivariate curve resolution is extended to the analysis of three-way data matrices. The particular case of three-way data where only one of the orders is common between slices is studied in some detail.

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Application of equality constraints on variables during alternating least squares procedures

Benthem

Keenan

Haaland

2002

Journal of Chemometrics

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We describe several methods of applying equality constraints while performing procedures that employ alternating least squares. Among these are mathematically rigorous methods of applying equality constraints, as well as approximate methods, commonly used in chemometrics, that are not mathematically rigorous. The rigorous methods are extensions of the methods described in detail in Lawson and Hanson's landmark text on solving least squares problems, which exhibit well-behaved least squares performance. The approximate methods tend to be easy to use and code, but they exhibit poor least squares behaviors and have properties that are not well understood. This paper explains the application of rigorous equality-constrained least squares and demonstrates the dangers of employing non-rigorous methods. We found that in some cases, upon initiating multivariate curve resolution with the exact basis vectors underlying synthetic data overlaid with noise, the approximate method actually results in an increase in the magnitude of residuals. This phenomenon indicates that the solutions for the approximate methods may actually diverge from the least squares solution.

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Self-modelling curve resolution in studies of spectrometric titrations of multi-equilibria systems by factor analysis

Cited by 65 publications

References 17 publications

Improved Materials Aging Diagnostics and Mechanisms through 2D Hyperspectral Imaging Methods and Algorithms

Improved Materials Aging Diagnostics and Mechanisms through 2D Hyperspectral Imaging Methods and Algorithms

Selectivity, local rank, three‐way data analysis and ambiguity in multivariate curve resolution

Application of equality constraints on variables during alternating least squares procedures

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