Rank annihilation with incomplete information

Burns, David H.; Callis, James B.; Christian, Gary D.

doi:10.1021/ac00126a049

Cited by 22 publications

(5 citation statements)

References 31 publications

(36 reference statements)

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“…Sanchez and Kowalski extended the method to the general case of several components that are not necessarily present in both the calibration and the unknown samples, obtained the solution by solving a generalized eigenproblem and called the method generalized rank annihilation method (GRAM) [38]. RAFA is used to analyze the two-way chromatographic spectral data [39], for determination environmental pollutants such as polyring aromatic compounds [40,41] and recently for spectrophotometric study of chemical kinetics [42] and the correction of several types of instrumental inconsistencies [43].…”

Section: Introductionmentioning

confidence: 99%

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

Abdollahi

Nazari

2003

Analytica Chimica Acta

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Section: Introductionmentioning

confidence: 99%

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

Abdollahi

Nazari

2003

Analytica Chimica Acta

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“…Another technique recently described in the literature can also correct for unknown background contributions. Burns, Callis, and Christian have described a rank annihilation method based on incomplete information that would be amenable to the type of chromatographic-spectroscopic data sets described here (19). That method presumes, however, that the known pure component responses can be modeled accurately, while the derivative-adaptive Kalman filtering approach employed here may be able to compensate for some errors in modeling these pure component responses.…”

Section: Resultsmentioning

confidence: 99%

Factor analysis and Kalman filter studies of severely overlapped amino acid derivatives in thin-layer chromatography

Rutan¹,

Motley²

1987

Anal. Chem.

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The performance of several mathematical approaches for quantification of components in cases of severe chromatographic and spectroscopic overlap has been investigated. The problem under consideration was the separation of two amino acids, glycine and glutamine, on high-performance thin-layer chromatographic plates, followed by derivatiration with o-phthaidiaidehyde. The chromatographic characteristics of these two amlno acids are very similar, and the fluorescence responses of the two derivatives are very similar as well. Here, five approaches, based on two data analysis methods, factor analysis and Kaiman filtering, have been studied. Each approach was able to detect the presence of the two amino acids in a mixture chromatogram, and the resolved responses showed a peak-shaped morphology. The concentration estimates were within an order of magnitude of the correct values, with the results for the derivativeadaptive Kaiman filtering approach showing the smallest errors, 5.9% error for glycine and -6.4% for glutamine.In the past several years, mathematical and statistical tools have been used increasingly to enhance the analysis of chemical data. In particular, several methods have been developed for the resolution of overlapped responses, which can arise in chromatographic and spectroscopic methods of analysis. In many cases, chromatographic methods can be coupled with multiwavelength spectroscopic detection approaches to enhance the analyst's ability to distinguish a number of coeluting components. Two classes of curve resolution approaches have been employed those that require a model for the spectral or chromatographic characteristics and those that are "self-modeling". The model-based curve resolution approaches are most useful for determining the relative contributions of each of the coeluting components to the overall spectroscopic response in cases where the identities of the contributing chemical species are known. These approaches include factor analysis methods ( l ) , linear leastsquares methods (2,3), modified least-squares approaches (4, 5), and Kalman filtering techniques (6, 7). One major requirement for successful implementation of all of these techniques is that the responses due to each of the components must be linearly independent of one another. This requirement means that inaccurate concentration estimates may be obtained for compounds that cannot be resolved chromatographically and that give rise to very similar spectral responses.One area where severely overlapped chromatographic and spectroscopic responses may cause difficulties in obtaining accurate concentration estimates is when derivatization methods are employed in chromatography to increase the detection sensitivity. In particular, fluorogenic reagents are often used to form fluorescent molecules from nonfluorescent Present address:analytes. The spectroscopic characteristics of these fluorescent derivatives are usually very similar, due to the fact that the energy levels in the fluorescent moiety are not substantially perturbed by th...

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“…Rank annihilation factor analysis is an efficient chemometric technique based on rank analysis for two-way data and can be employed in several forms for solving various problems in chemistry (20)(21)(22)(23)(24). RAFA was originally developed by Ho et al as an iterative procedure (20).…”

Section: Rank Annihilation Factor Analysismentioning

confidence: 99%

Soft‐modeling based spectrofluorimetric study of simultaneous equilibria

Abdollahi

Sajjadi

2009

Luminescence

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A two-way soft resolution method will fail when applied to a simultaneous equilibria system due to rank deficiency in its concentration profiles. Increasing the dimensionality of measurements from two-way to three-way data can be used to overcome this problem. Simultaneous dissociation of two weak acids is considered as a model for simultaneous equilibria. Three-way data obtained from excitation-emission spectrofluorimetric monitoring of a pH-metric titration is analyzed using a proper combination of well-known soft-modeling methods. Multivariate curve resolution-alternating least squares is used for calculating the excitation and emission spectral profiles of involved species and rank annihilation factor analysis for obtaining the contribution of each species in measured excitation-emission matrices at different pHs. The results of simulated and real simultaneous acids dissociation equilibria showed that the proposed combined method performs well even in situation when the equilibrium constants are close to each other. The applicability of method for study of an acidic dissociation is also shown.

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Rank annihilation with incomplete information

Cited by 22 publications

References 31 publications

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

Rank annihilation factor analysis for spectrophotometric study of complex formation equilibria

Factor analysis and Kalman filter studies of severely overlapped amino acid derivatives in thin-layer chromatography

Soft‐modeling based spectrofluorimetric study of simultaneous equilibria

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