Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer

Ho, C. N.; Christian, Gary D.; Davidson, Ernest R.

doi:10.1021/ac00224a024

Cited by 86 publications

(36 citation statements)

References 17 publications

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“…In order to find this k-value an iterative procedure is used which plots the eigenvalues (or singular values, SVs) of the least significant factor of D residual as a function of k. This eigenvalue becomes minimal when k exactly compensates the signal of the analyte in the sample. For other k-values the signal is under or overcompensates which result in higher value of the eigenvalue (or SV) [13][14][15]32]. In this work the algorithm of RAFA is employed to analyze different spectra of the sample matrix (DD) using calibration standard matrices of analyte (DD standard ).…”

Section: Rank Annihilation Factor Analysismentioning

confidence: 99%

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Bahram¹,

Mabhooti²

2009

Journal of Chemometrics

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aIn this work rank annihilation factor analysis (RAFA) is used to analyze difference spectra of kineticspectrophotometric data. Annihilation of the contribution of one chemical component from the original data matrix is a general method in RAFA. However, sometimes RAFA is not suitable for studying rank deficient data such as kinetic-spectrophotometric measurements. On the other hand, in order to apply RAFA for the determination of an analyte in an unknown sample, a standard two-way matrix of the analyte with rank one should generally be available. This is not usually attainable for kinetic-spectrophotometric monitoring of complexation reactions. Processes monitored by difference spectroscopy always have the spectrum of the initial stage subtracted from each spectrum in the data matrix. In this work we show that, for kinetic-spectrophotometric data of complexation reactions, the spectrum of ligand (reactant) itself can be used as initial spectrum for subtraction. The obtained difference matrix of sample and that of analyte of interest will be full-rank and rank 1, respectively. Therefore the system can be analyzed by RAFA. The proposed method was investigated with simulated data at the first stage. The method was then applied in the analysis of experimental kinetic-spectrophotometric data of a complexation reactions of Co(II) and Ni(II) with chromogenic reagent 1-(2-pyridylazo) 2-naphthol in order to do multi-component determination of these ions in various real samples.

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Section: Rank Annihilation Factor Analysismentioning

confidence: 99%

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Bahram¹,

Mabhooti²

2009

Journal of Chemometrics

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“…constant variance) measurement noise the unknown sample data matrix can be expressed asM =M+dM (3) where dM denotes the Iϫ J matrix of measurement errors in M . The assumption of uncorrelated, homoscedastic measurement noise implies that (6) where N stands for the standard deviation of the measurement noise in Ñ .…”

Section: Propagation Of Uncorrelated Homoscedastic Instrumental Errorsmentioning

confidence: 99%

“…Building on the work of Ho et al [1][2][3] and Lorber, 4 Sanchez and Kowalski 5 developed a method for quantitative and qualitative multicomponent analysis. Their method, the generalized rank annihilation method (GRAM), performs the task of calibrating for the desired analytes in the presence of unknown interferents.…”

Section: Introductionmentioning

confidence: 99%

Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated

1997

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SUMMARYThe generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that uses two data matrices simultaneously, i.e. one for the unknown and one for the calibration sample. The method is known to become an eigenvalue problem for which the eigenvalues are the ratios of the concentrations for the samples under scrutiny. Previously derived standard errors in the estimated eigenvalues of GRAM have very recently been shown to be based on unrealistic assumptions about the measurement errors. In this paper a systematic notation is introduced that enables the propagation of errors that are based on realistic assumptions concerning the datagenerating process. The error propagation will be performed in detail for the case that one data order modulates the second one. Extensions to more complicated error models are indicated.

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“…Rank annihilation factor analysis (RAFA) is an effective chemometric tool that the idea behind it, is the rank analysis of two way spectrum data, and quantitatively can be used to analysis of mix systems with unknown background. The original algorithm of RAFA was written by Ho et al and applied on one and two component mixtures of perylene and anthracene [20][21][22]. They showed that they were able to determine the concentration of one analyte in presence of the other using only one pure standard and using fluorescence excitation emission landscapes [23].…”

Section: Introductionmentioning

confidence: 99%

Application of central composite design and rank annihilation factor analysis for optimization of mixed chelate of UO₂ ²⁺ complex with ammonium-N,N-tetramethylenedithiocarbamate and estimation of K_f value

Aslani¹,

Kuru²,

Aslani³

2015

Radiochimica Acta

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Abstract:The interaction between UO 2+ 2 and ammonium-N,N-tetramethylenedithiocarbamate (ATMDTC) was investigated experimentally by means of UV-Vis spectrophotometry. Central Composite Design (CCD) was applied to optimisation of reaction with 54 runs in duplicate. This design type was also used to developed mathematical model equation. Analysis of Variance (ANOVA) indicates that the terms of the model are significant within the 95% confident interval. Remarkably initial solution pH, initial AT-MDTC concentration, initial Cu 2+ concentration and temperature have effect on the reaction. Formation constant (log f ) was calculated as 2.917 by using Rank Annihilation Factor Analysis (RAFA).

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Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer

Cited by 86 publications

References 17 publications

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated

Application of central composite design and rank annihilation factor analysis for optimization of mixed chelate of UO₂ ²⁺ complex with ammonium-N,N-tetramethylenedithiocarbamate and estimation of K_f value

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Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer

Cited by 86 publications

References 17 publications

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated

Application of central composite design and rank annihilation factor analysis for optimization of mixed chelate of UO2 2+ complex with ammonium-N,N-tetramethylenedithiocarbamate and estimation of Kf value

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Application of central composite design and rank annihilation factor analysis for optimization of mixed chelate of UO₂ ²⁺ complex with ammonium-N,N-tetramethylenedithiocarbamate and estimation of K_f value