The price paid for the second‐order advantage when using the generalized rank annihilation method (GRAM)

Faber, Nicolaas M.

doi:10.1002/cem.688

Cited by 25 publications

(21 citation statements)

References 22 publications

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“…They are understood by resorting to the useful concept of net analyte signal (NAS), first developed by Lorber. 37 The sensitivity (SEN) for a particular analyte is estimated as the net analyte signal at unit concentration; the following equation seems to apply to the presently studied case: 38 …”

Section: Figures Of Meritmentioning

confidence: 99%

Determination of Indole-3-Acetic Acid in Soil Using Excitation–Emission Matrix Fluorescence with Trilinear Decomposition-based Calibration Methods

Zhu

Nie

et al. 2009

ANAL. SCI.

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Indole-3-acetic acid (IAA) is a phytohormone of the auxin group and is capable of coordinating the overall processes of plant growth and development. IAA is active in the very low concentration range. Therefore, it is important to quantify IAA in the low concentration range in complex system. In this work, a new spectrofluorometric method for the direct determination of IAA in soil is proposed and discussed. It combines the fluorescence excitation-emission matrices (EEMs) with second-order calibration methods based on the alternating trilinear decomposition (ATLD) algorithm and the self-weighed alternating trilinear decomposition (SWATLD) algorithm. These methodologies fully exploit the secondorder advantage of the three-way fluorescence data, allowing the analyte concentrations to be quantified even in the presence of unknown fluorescent interferents. IAA recoveries in soil were determined as 100.6 ± 3.0 and 96.9 ± 1.1% with ATLD and SWATLD, respectively. The limits of detection obtained were 17.6 and 4.6 ng mL -1 , and the limits of quantification were 52.9 and 13.9 ng mL -1 with ATLD and SWATLD, respectively.

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Section: Figures Of Meritmentioning

confidence: 99%

Determination of Indole-3-Acetic Acid in Soil Using Excitation–Emission Matrix Fluorescence with Trilinear Decomposition-based Calibration Methods

Zhu

Nie

et al. 2009

ANAL. SCI.

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“…48 Different approaches have been discussed in the literature for computing the figures of merit for higher-order methodologies. [49][50][51][52] As for the sensitivity (SEN), the following equation seems to apply to the presently studied case: [53][54][55] …”

Section: Figures Of Meritmentioning

confidence: 99%

“…Notice that the full sensitivities decrease in the presence of other sample constituents, by a degree that depends on the profile overlapping. The selectivity (SEL), in turn, is the ratio between the sensitivity and the total signal, and can be estimated as [53][54][55] …”

Section: Sen = K{[(a T A)*(b T B)]mentioning

confidence: 99%

Determination of Daunomycin in Human Plasma and Urine by Using an Interference-free Analysis of Excitation-Emission Matrix Fluorescence Data with Second-Order Calibration

et al. 2006

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IntroductionDaunorubicin (DNR), discovered in the early 1960s, is an anthracycline antibiotic with antiblastic and anticancer activity, which is linked by the formation of intercalative complexes with DNA and the inhibition of both DNA and RNA synthesis. Although it still remains an important component for many current chemotherapy protocols of acute and myelogenous leukemia, cardiotoxicity is a serious problem, especially in the case of overdoses.1 It is thus important for determining DNR in human plasma and urine. Various instrumental methods, such as polarography, 2 high-performance liquid chromatography, 3-5 the enzymatic immunological method, 6 voltammetry, 7 capillary electrophoresis, 8,9 and electrospray ionization mass spectrometry 10 have been reported for DNR determination in biological fluids and in dosage forms. However, these methods are either troublesome or time-consuming.With the development of modern analytical instrumentation that generate a multidimensional data array for each sample, multiway data arrays have been prominently useful for the quantitative analysis of complex multicomponent samples. Particularly, three-way data arrays following the trilinear model, such as excitation-emission fluorescence matrices, have been gaining widespread analytical acceptance. 11Although, interestingly, there are many models for three-way data arrays, only the PARAFAC model ensures uniqueness in a straightforward way. 12In addition, the decomposition of a three-way data array built with response matrices measured for many samples is often unique, allowing relative concentrations and spectral profiles of individual sample components to be extracted directly. That is, the analysis of several components of interest can be quantified even in the presence of unknown interferents, commonly called the "second-order advantage". 13,14The different multiway methods used to resolve multicomponent mixtures belong to three main groups. The first group is direct solution. It is to resolve the data arrays by utilizing an eigenanalysis-based procedure, which typically works well when the signal-to-noise ratio is high. The generalized rank annihilation method (GRAM) 15-17 and the direct trilinear decomposition (DTLD) method 18-20 are wellknown examples. Unfortunately, GRAM is constrained to use only one standard and one mixture sample at a time. Although the DTLD method takes into account a direct solution through multiple samples, it is required to construct two pseudosamples, which unavoidably results in the loss of information in multiple samples. In addition, these methods may occasionally produce imaginary solutions and exhibit inflated variance. The second main group includes least-squares methods. Bilinear least squares (BLLS) is a recently introduced technique, based on a direct least-squares procedure. 21,22 The third main group is an iterative one. 12,23-40 Iterative algorithms have been widely employed. The PARAFAC algorithm proposed by Harshman 34 is a representative method of the third group. These have succ...

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“…Different approaches have been discussed in the literature for computing the figures of merit. [58][59][60][61] As for the sensitivity, the following equation seems to apply to the presently studied case: [62][63][64] …”

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Determination of Psoralen in Human Plasma Using Excitation-Emission Matrix Fluorescence Coupled to Second-order Calibration

et al. 2008

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Psoralea, as a Chinese medicinal herb, is distributed throughout the world. Psoralen, a heterocyclic aromatic compound, is one of the main active ingredients of psoralea, and is increasingly being utilized in dermatology for the photochemotherapy of diseases.1-3 The use of psoralen in medicine has been associated with a higher incidence of skin cancer. 4,5 Therefore, it is significant to quantify psoralen (PSO) in biological fluids. Several HPLC methods have been reported for the determination of psoralens [6][7][8][9][10][11][12] in callus cultures, vitro culture, plants, and citrus essential oils. The gas chromatography method has been demonstrated for determination of psoralens in phytomedicines. 13 However, these methods are either troublesome or timeconsuming. It is necessary to explore more simple methods for the determination of PSO in complicated systems.With the increasing popularity of advanced instrumentation that generates multidimensional data array for each sample, trilinear decomposition models have become an area of much current activity in chemometrics research. [14][15][16][17][18] The attractive merit derived from three-way data arrays is attributed to that several components of interest can be quantified even in the presence of unknown interferents, usually called a "secondorder advantage". [19][20][21] Generally, algorithms for the decomposition of three-way data arrays can be divided into two categories. One approach is based on generalized eigenanalysis to resolve the data arrays, which typically works well when the signal-to-noise ratio is high, with the well-known examples of the generalized rank annihilation method (GRAM) 22-24 and the direct trilinear decomposition (DTLD) method. [25][26][27] Unfortunately, GRAM is constrained to use only one standard and one mixture sample at a time. Although the DTLD method allows for a direct solution through multiple samples, it requires the construction of two pseudosamples, which unavoidably causes a loss of information in multiple samples.Furthermore, these approaches may occasionally yield imaginary solutions and exhibit inflated variance. An alternative approach is an iterative one, [28][29][30][31][32][33][34][35][36][37][38][39][40][41] represented by parallel factor analysis (PARAFAC), proposed by Harshman. 38These have successfully solved many practical problems, such as environmental monitoring, 42 This paper describes a newly developed approach, an alternating normalization-weighted error (ANWE) method, and PARAFAC for the trilinear analysis of excitation-emission matrix fluorescence data. The results demonstrated that the determination of PSO can be conveniently achieved in plasma samples using excitation-emission matrix fluorescence coupled to second-order calibration, and that the performance of the ANWE method is similar or better than that of PARAFAC. NomenclatureThroughout this paper, scalars are represented by lower-case italics: bold lower-case characters mean vectors; bold capitals designate two-way matrices; underlined bold ...

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The price paid for the second‐order advantage when using the generalized rank annihilation method (GRAM)

Cited by 25 publications

References 22 publications

Determination of Indole-3-Acetic Acid in Soil Using Excitation–Emission Matrix Fluorescence with Trilinear Decomposition-based Calibration Methods

Determination of Indole-3-Acetic Acid in Soil Using Excitation–Emission Matrix Fluorescence with Trilinear Decomposition-based Calibration Methods

Determination of Daunomycin in Human Plasma and Urine by Using an Interference-free Analysis of Excitation-Emission Matrix Fluorescence Data with Second-Order Calibration

Determination of Psoralen in Human Plasma Using Excitation-Emission Matrix Fluorescence Coupled to Second-order Calibration

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