Some theoretical results on second‐order calibration methods for data with and without rank overlap

Kiers, Henk A.L.; Smilde, Age K.

doi:10.1002/cem.1180090305

Cited by 50 publications

(29 citation statements)

References 13 publications

(3 reference statements)

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“…in the field of chemometrics, especially owing to its highly attractive uniqueness property. In certain applications of curve resolution [5,6] and secondorder calibration [7,8], this uniqueness of the PARAFAC model is essential for solving the problems. A major practical obstacle in the use of the PARAFAC model is how to determine the appropriate number of components.…”

Section: Introductionmentioning

confidence: 99%

A new efficient method for determining the number of components in PARAFAC models

Bro¹,

Kiers

2003

Journal of Chemometrics

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A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the`appropriateness' of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension-wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete.

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Section: Introductionmentioning

confidence: 99%

A new efficient method for determining the number of components in PARAFAC models

Bro¹,

Kiers

2003

Journal of Chemometrics

Self Cite

1,121

718

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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 parallel factor analysis (PARAFAC) [17][18][19][20][21] algorithm is one of the most popular methods in the decomposition of three-way data. There were also some other versions to improve PARAFAC, 10,22,23 which were attempted to provide improved results.…”

Section: Introductionmentioning

confidence: 99%

An Improved Trilinear Decomposition Algorithm Based on a Lagrange Operator

Jiang

Long

et al. 2003

ANAL. SCI.

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An improved trilinear decomposition algorithm based on a Lagrange operator (LO) is developed in this paper, which introduces a Lagrange operator and penalty terms in the loss function to improve the performance of the algorithm. Compared to the traditional parallel factor (PARAFAC) algorithm, the algorithm not only may converge much faster, but also overcome the sensibility to estimate the number of components. A set of simulated and measured excitation/emission fluorescence data were treated by both the proposed and traditional PARAFAC algorithm to compare their efficiencies. The analytical results obtained with real chemical system containing aspirin and its metabolic products show that the trilinear decomposition methodology is a promising tool to obtain spectral and composition information from mixtures without chemical separation.

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Some theoretical results on second‐order calibration methods for data with and without rank overlap

Cited by 50 publications

References 13 publications

A new efficient method for determining the number of components in PARAFAC models

A new efficient method for determining the number of components in PARAFAC models

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

An Improved Trilinear Decomposition Algorithm Based on a Lagrange Operator

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