Three- and four-way parallel factor (PARAFAC) analysis of photochemically induced excitation–emission kinetic fluorescence spectra

Nahorniak, Michelle L.; Cooper, G.; Kim, Yoon-Chang; Booksh, Karl S.

doi:10.1039/b409235j

Cited by 53 publications

(35 citation statements)

References 26 publications

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“…However, there is no clear trend which wavelet type achieves the smallest cubes or the highest acceleration. As will be discussed later in this study, the initialization of the PARAFAC algorithm with random values has a strong impact on the acceleration as the number of iterations varies until convergence is obtained (4). In general, low-compression methods result in more precise models than high-compression levels.…”

Section: Resultsmentioning

confidence: 97%

“…Then the nth triad is spanned by an analyte's emission spectrum, x n , excitation spectrum, y n , and a vector z n containing the nth analyte concentrations. Some fluorescent polyaromatic hydrocarbons show photocatalyticaly induced, time dependent fluorescence [4,5]. Such data sets have four ways, that is excitation and emission wavelength, time profiles of fluorescence decay/increase and sample (or concentration).…”

Section: Resultsmentioning

confidence: 99%

“…For determining the appropriate number of factors, N, there was no need to apply CORCONDIA because for synthetic hypercubes N ¼ 2 was known due to data generation and for the experimental data set N ¼ 3 had been determined in Reference [4].…”

Section: Methods For Assessing the Algorithm And Resulting Modelsmentioning

confidence: 99%

“…Exemplary 4D hypercube acquired by EEM spectroscopy [4,5]; such a hypercube consists of a series of the 3D cubes; every 3D cube in turn belongs to one sample and contains a time series of EEM spectra.…”

Section: Wavelet Compression Of Multi-way Data Setsmentioning

confidence: 99%

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Accelerating the analyses of 3‐way and 4‐way PARAFAC models utilizing multi‐dimensional wavelet compression

Cramer

Kim

Vogt

et al. 2005

Journal of Chemometrics

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Parallel factor analysis (PARAFAC) is one of the most popular methods for evaluating multi-way data sets, such as those typically acquired by hyphenated measurement techniques. One of the reasons for PARAFAC popularity is the ability to extract directly interpretable chemometric models with little a priori information and the capability to handle unknown interferents and missing values. However, PARAFAC requires long computation times that often prohibit sufficiently fast analyses for applications such as online sensing. An additional challenge faced by PARAFAC users is the handling and storage of very large, high-dimensional data sets. Accelerating computations and reducing storage requirements in multi-way analyses are the topics of this manuscript. This study introduces a data pre-processing method based on multi-dimensional wavelet transforms (WTs), which enables highly efficient data compression applied prior to data evaluation. Because multidimensional WTs are linear, the intrinsic underlying linear data construction is preserved in the wavelet domain. In almost all studied examples, computation times for analyzing the much smaller, compressed data sets could be reduced so much that the additional effort for wavelet compression was more than recompensated. For 3-way and 4-way synthetic and experimental data sets, acceleration factors up to 50 have been achieved; these data sets could be compressed down to a few per cent of the original size. Despite the high compression, accurate and interpretable models were derived, which are in good agreement with conventionally determined PARAFAC models. This study also found that the wavelet type used for compression is an important factor determining acceleration factors, data compression ratios and model quality.

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Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

Section: Methods For Assessing the Algorithm And Resulting Modelsmentioning

confidence: 99%

Section: Wavelet Compression Of Multi-way Data Setsmentioning

confidence: 99%

See 2 more Smart Citations

Accelerating the analyses of 3‐way and 4‐way PARAFAC models utilizing multi‐dimensional wavelet compression

Cramer

Kim

Vogt

et al. 2005

Journal of Chemometrics

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“…28,29 Nevertheless, the complete "third-order advantage", or the Nth-order advantage, is still unknown totally. 1 To the best of our knowledge, only a few algorithms, such as four-way PARAFAC, 30,31 trilinear least-squares (TLLS), 32 alternating penalty quadrilinear decomposition (APQLD), 33 alternating weighted residue constraint quadrilinear decomposition (AWRCQLD), 34 can be used for the third-order calibration of four-way data. Accordingly, to search for the "third-order advantage", more related studies on four-way data analysis and third-order calibration are worth further investigation.…”

Section: Introductionmentioning

confidence: 99%

Four-way Self-weighted Alternating Normalized Residue Fitting Algorithm with Application for the Analysis of Serotonin in Human Plasma

Liu

Kang

et al. 2012

ANAL. SCI.

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Evaluation of variation matrix arrays by parallel factor analysis

Abdollahi

Sajjadi

2008

Journal of Chemometrics

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a PARAFAC is one of the most widely used algorithms for trilinear decomposition. The uniqueness properties of the PARAFAC model are very attractive regardless of whether one is interested curve resolution or not. The fact that PARAFAC provides one unique solution simplifies interpretation of the model. But in three-way data arrays the uniqueness condition can only be expected when k A R k B R k C ‡ 2F R 2, where F is the number of components and k's are the Kruskal ranks of loadings A to C. As much as second order instruments produce data of varying complexity depending upon the nature of the analytical techniques being combined, with some three-way data it is possible for patterns generated by the underlying sources of variation to have sufficient independent effects in two modes, yet nonetheless be proportional in a third mode. For example, in three-way data for spectrophotometric titrations of weak acids or bases (pH-wavelength-sample), a rank deficiency may occur in two modes, that is closure rank deficiency in the pH mode and proportionality rank deficiency in the sample direction because each analyte will have acidic and basic forms that are linear combinations in the sample mode. The goal of the present paper is to overcome the non-uniqueness problem in the second order calibration of monoprotic acids mixtures. The solution contains two steps: first each pH-absorbance matrix is pretreated by subtraction of the first spectrum from each spectrum in the data matrix. This pretreated data matrix is called the variation matrix. Second, by stacking the variation matrices, a three-way trilinear variation data array will be obtained without the proportional linear dependency problem that can be resolved uniquely by PARAFAC. It is shown, although unique results are not guaranteed by the Kruscal's condition for the original three-way data, this condition is fulfilled for pretreated three-way data. Hence, the variation array may be uniquely decomposed by the PARAFAC algorithm. Studies on simulated as well as real data array reveal the applicability of the proposed method to this kind of problem in the second order calibration of monoprotic acids.

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Three- and four-way parallel factor (PARAFAC) analysis of photochemically induced excitation–emission kinetic fluorescence spectra

Cited by 53 publications

References 26 publications

Accelerating the analyses of 3‐way and 4‐way PARAFAC models utilizing multi‐dimensional wavelet compression

Accelerating the analyses of 3‐way and 4‐way PARAFAC models utilizing multi‐dimensional wavelet compression

Four-way Self-weighted Alternating Normalized Residue Fitting Algorithm with Application for the Analysis of Serotonin in Human Plasma

Evaluation of variation matrix arrays by parallel factor analysis

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