Duality based direct resolution of unique profiles using zero concentration region information

Tavakkoli, Elnaz; Rajkó, Róbert; Abdollahi, Hamid

doi:10.1016/j.talanta.2018.03.022

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…The p parameter (number of basis vectors) has to be chosen by user. To avoid the influence of initial approximation, 22,25 we used the decomposition yielding the highest explained variance among 100 runs to obtain a reliable factorization (following recommendations 26,46 ). The nmf_bpas function from the "linear-algebra" package for GNU Octave was used for computations.…”

Section: Data Pre-treatmentmentioning

confidence: 99%

“…22 Recent years have also seen a growing interest in non-negative matrix factorization (NMF), which was originally developed for the analysis of images. 23,24 As its name implies, all the resulting matrices are constrained to be non-negative 22,25,26 while the orthogonality of components is not required, which is reasonable when working with spectroscopic data and brings the decomposition closer to physical reality. On the other hand, an NMF decomposition results in an infinite set of solutions due to the so-called rotational ambiguity.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, an NMF decomposition results in an infinite set of solutions due to the so-called rotational ambiguity. 22,25 Therefore, multiple (10–1000) algorithm runs are needed to obtain a reliable factorisation. 26 The independent component analysis (ICA) was initially used for BSS in neurophysiology 27 and now found many successful applications in technics and information technology, 28 as well as in analytical fluorescence, nuclear magnetic resonance (NMR), near- and mid-infrared (NIR, MIR) and Raman spectroscopy, chromatography and electrochemistry.…”

Section: Introductionmentioning

confidence: 99%

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A novel approach for discovering correlations between elemental and molecular composition using laser-based spectroscopic techniques

Sushkov

Galbács

Fintor

et al. 2022

Analyst

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Section: Data Pre-treatmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel approach for discovering correlations between elemental and molecular composition using laser-based spectroscopic techniques

Sushkov

Galbács

Fintor

et al. 2022

Analyst

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“…NMF does not require its latent vectors to be orthogonal, which is a benefit for mixtures sharing some signals, but the solution is not unique. In other words, decomposition results in an infinite set of solutions due to the so-called rotational ambiguity [ 35 , 36 ]. On the other hand, the solution is always non-negative, which is convenient when working with many spectroscopic techniques (such as LIBS and Raman spectroscopy) where signals cannot be negative; NMF thus gives only those solutions that can be physically valid.…”

Section: Introductionmentioning

confidence: 99%

Towards Automated Classification of Zooplankton Using Combination of Laser Spectral Techniques and Advanced Chemometrics

Sushkov

Galbács

Janovszky

et al. 2022

Sensors

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Zooplankton identification has been the subject of many studies. They are mainly based on the analysis of photographs (computer vision). However, spectroscopic techniques can be a good alternative due to the valuable additional information that they provide. We tested the performance of several chemometric techniques (principal component analysis (PCA), non-negative matrix factorisation (NMF), and common dimensions and specific weights analysis (CCSWA of ComDim)) for the unsupervised classification of zooplankton species based on their spectra. The spectra were obtained using laser-induced breakdown spectroscopy (LIBS) and Raman spectroscopy. It was convenient to assess the discriminative power in terms of silhouette metrics (Sil). The LIBS data were substantially more useful for the task than the Raman spectra, although the best results were achieved for the combined LIBS + Raman dataset (best Sil = 0.67). Although NMF (Sil = 0.63) and ComDim (Sil = 0.39) gave interesting information in the loadings, PCA was generally enough for the discrimination based on the score graphs. The distinguishing between Calanoida and Euphausiacea crustaceans and Limacina helicina sea snails has proved possible, probably because of their different mineral compositions. Conversely, arrow worms (Parasagitta elegans) usually fell into the same class with Calanoida despite the differences in their Raman spectra.

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“…It is important to notice that a careful design of the augmented data set, should include, if possible, samples containing single pure analytes or pure interferents. This might allow the decomposition to reach unique solutions using the species correspondence constraint, also called the sample selectivity constraint, which forces resolved concentration profiles to have zero area for the known absent species in certain samples as a consequence of the well-known Manne theorems. − …”

mentioning

confidence: 99%

Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods

2018

Self Cite

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A novel procedure is described for processing the second-order data matrices with multivariate curve resolution-alternating least-squares; while the data set is nontrilinear and severe profile overlapping occurs in the instrumental data modes. The area of feasible solutions can be reduced to a unique solution by including/considering the area correlation constraint, besides the traditional constraints (i.e., non-negativity, unimodality, species correspondence, etc.). The latter is implemented not only for the unknown samples but also for all calibration samples, regardless of their interferent content. The area of correlation constraint was specially designed to remove rotational ambiguity in the chemical data sets when information about calibration samples is at hand. In this contribution a comprehensive strategy is developed to uniquely unravel nontrilinear data sets or data sets with severely overlapped profiles in the instrumental data modes. The approach is illustrated with simulated and experimental data sets. Borgen plots are employed to adequately visualize the extent of rotational ambiguity under non-negativity constraint.

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Duality based direct resolution of unique profiles using zero concentration region information

Cited by 8 publications

References 21 publications

A novel approach for discovering correlations between elemental and molecular composition using laser-based spectroscopic techniques

A novel approach for discovering correlations between elemental and molecular composition using laser-based spectroscopic techniques

Towards Automated Classification of Zooplankton Using Combination of Laser Spectral Techniques and Advanced Chemometrics

Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods

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