An Improved Trilinear Decomposition Algorithm Based on a Lagrange Operator

Lu, Jian-Zhong; Jiang, Jian‐Hui; Long, Ning; Mo, Cui-Yun; Yu, Ru‐Qin

doi:10.2116/analsci.19.1037

Cited by 6 publications

(4 citation statements)

References 31 publications

(27 reference statements)

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“…A better understanding of how to objectively select the appropriate number of factors is an area of great interest in application of PARAFAC to trilinear and higher order data − and is critical for automated data processing using PARAFAC. Notable effort has gone into the creation of PARAFAC algorithms that are less susceptible to errors in selecting the correct number of factors. − Usually it is sufficient to select a number of factors in the PARAFAC model equal to the number of interferences plus the number of analytes present in the data. , However, the number of analytes and interferences is often not known, and it can be difficult to a priori predict an appropriate number of factors to yield a suitable model. The case of deconvolution of an analyte having a low signal-to-noise ratio (S/N) is especially challengingcontributions to the total signal from noise can have enough trilinearity to require a highly variable number of additional factors among replicates, each factor describing some contribution to the total signal due to noise, in order to have enough factors so the relatively small analyte signal is sufficiently modeled.…”

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confidence: 99%

Parallel Factor Analysis (PARAFAC) of Target Analytes in GC × GC−TOFMS Data: Automated Selection of a Model with an Appropriate Number of Factors

Synovec

2007

Anal. Chem.

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PARAFAC (parallel factor analysis) is a powerful chemometric method that has been demonstrated as a useful deconvolution technique in dealing with data obtained using comprehensive two-dimensional gas chromatography combined with time-of-flight mass spectrometry (GC x GC-TOFMS). However, selection of a PARAFAC model having an appropriate number of factors can be challenging, especially at low S/N or for analytes in the presence of chromatographic and spectral overlapping compounds (interferences). Herein, we present a method for the automated selection of a PARAFAC model with an appropriate number of factors in GC x GC-TOFMS data, demonstrated for a target analyte of interest. The approach taken in the methodology is as follows. PARAFAC models are automatically generated having an incrementally higher number of factors until mass spectral matching of the corresponding loadings in the model against a target analyte mass spectrum indicates overfitting has occurred. Then, the model selected simply has one less factor than the overfit model. Results indicate this model selection approach is viable across the detection range of the instrument from overloaded analyte signal down to low S/N analyte signal (total ion current signal intensity at analyte peak maximum S/N < 1). While the methodology is generally applicable to comprehensive two-dimensional separations using multichannel spectral detection, we evaluated it with several target analytes using GC x GC-TOFMS. For brevity in this report, only results for bromobenzene as target analyte are presented. Alternatively, instead of using the model with one less factor than the overfit model, one can select the model with the highest mass spectral match for the target analyte from among all the models generated (excluding the overfit model). Both model selection approaches gave essentially identical results.

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confidence: 99%

Parallel Factor Analysis (PARAFAC) of Target Analytes in GC × GC−TOFMS Data: Automated Selection of a Model with an Appropriate Number of Factors

Synovec

2007

Anal. Chem.

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“…21,22 The third main group is an iterative one. 12,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] Iterative algorithms have been widely employed. The PARAFAC algorithm proposed by Harshman 34 is a representative method of the third group.…”

Section: 14mentioning

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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“…The experimental results demonstrated that both algorithms, as promising quantitative alternatives, have been satisfactorily applied to the determination of sulpiride in human urine, but the performance of AFR was slightly better than that of SWATLD. Especially, three-way calibration algorithms, [14][15][16][17][18][19][20][21][22][23][24][25][26][27] such as parallel factor analysis (PARAFAC), 16,17 alternating trilinear decomposition (ATLD) 20 and self-weighted alternating trilinear decomposition (SWATLD), 21 are being increasingly utilized for the processing of three-way data following the trilinear component model. 17 One is able to extract relative concentrations and spectral profiles of individual components in mixture samples, since the methods enable unique decompositions of a three-way data array.…”

Section: Introductionmentioning

confidence: 99%

Determination of Sulpiride in Human Urine Using Excitation-Emission Matrix Fluorescence Coupled with Second-order Calibration

et al. 2007

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An Improved Trilinear Decomposition Algorithm Based on a Lagrange Operator

Cited by 6 publications

References 31 publications

Parallel Factor Analysis (PARAFAC) of Target Analytes in GC × GC−TOFMS Data: Automated Selection of a Model with an Appropriate Number of Factors

Parallel Factor Analysis (PARAFAC) of Target Analytes in GC × GC−TOFMS Data: Automated Selection of a Model with an Appropriate Number of Factors

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 Sulpiride in Human Urine Using Excitation-Emission Matrix Fluorescence Coupled with Second-order Calibration

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