Sufficient conditions for unique solutions within a certain class of curve resolution models

Smilde, Age K.; Hoefsloot, Huub C. J.; Kiers, Henk A.L.; Bijlsma, Sabina; Boelens, H.F.M.

doi:10.1002/cem.685

Cited by 28 publications

(17 citation statements)

References 29 publications

(25 reference statements)

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“…15 A drawback of MCR is that the solution is not unique, which means the temporal resolved spectra and decay profiles can be rotated without changing the residuals of the model, leading to an infinite number of solutions. 16 To solve this problem, constraints need to be embedded in MCR to obtain meaningful results. Traditionally, nonnegativity constraints are used for chemical and physical data to remove negative signals.…”

Section: Introductionmentioning

confidence: 99%

Real-life applications of the MULVADO software package for processing DOSY NMR data

Huo

Geurts²,

Brands³

et al. 2006

Magn. Reson. Chem.

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MULVADO is a newly developed software package for DOSY NMR data processing, based on multivariate curve resolution (MCR), one of the principal multivariate methods for processing DOSY data. This paper will evaluate this software package by using real-life data of materials used in the printing industry: two data sets from the same ink sample but of different quality. Also a sample of an organic photoconductor and a toner sample are analysed. Compared with the routine DOSY output from monoexponential fitting, one of the single channel algorithms in the commercial Bruker software, MULVADO provides several advantages. The key advantage of MCR is that it overcomes the fluctuation problem (non-consistent diffusion coefficient of the same component). The combination of non-linear regression (NLR) and MCR can yield more accurate resolution of a complex mixture. In addition, the data pre-processing techniques in MULVADO minimise the negative effects of experimental artefacts on the results of the data. In this paper, the challenges for analysing polymer samples and other more complex samples will also be discussed.

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Section: Introductionmentioning

confidence: 99%

Real-life applications of the MULVADO software package for processing DOSY NMR data

Huo

Geurts²,

Brands³

et al. 2006

Magn. Reson. Chem.

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show abstract

“…The disadvantage of most curve resolution method is that the solutions are not unique; i.e., there are infinite pure spectra and the decay profiles that can fulfil Eq. (4) with the same residuals between the constructed data and the original data [27]. This disadvantage can be overcome by applying non-negativity constraints to the solutions, which is described as the classic MCR in this paper.…”

Section: Simulated Data2mentioning

confidence: 91%

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

Huo

Wehrens

Buydens

2004

Journal of Magnetic Resonance

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“…Curve resolution is a class of mathematical techniques concerned with the estimation of pure profiles underlying a set of measurements . Unique decomposition does not hold in cases with ‘rank overlap’ .…”

Section: Theoretical Basismentioning

confidence: 99%

Visualization and establishment of partial uniqueness and uniqueness rules in parallel factor analysis

Omidikia

Abdollahi

Kompany‐Zareh

2013

Journal of Chemometrics

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Parallel factor analysis (PARAFAC) is believed to be one of the most widely used multiway curve resolution techniques. The superiority of PARAFAC is due to its uniqueness property that is provided under mild assumptions. Unambiguously recovered chemically and physically meaningful profiles by PARAFAC are reliable for quantitative and qualitative application. The essential uniqueness condition of PARAFAC breaks totally or partially in data sets with linearly dependent loadings. PARAFAC uniqueness levels include full uniqueness, partial uniqueness, uni‐mode uniqueness, and full non‐uniqueness. Although PARAFAC uniqueness conditions are more or less known, they cannot cover the whole of existing uniqueness problems, especially complex rank‐deficient systems. The questions investigated here are as follows: Under which conditions is PARAFAC still unique and what is the extent of deterioration of PARAFAC uniqueness by linearly dependent loadings? These are among the most important points in dealing with three‐way data arrays with PARAFAC models. Direct visualization of feasible bands using an explicit, well‐defined, and trustworthy method is a key feature of our approach to the investigation of uniqueness and recasting partial uniqueness rules in this study. Different simulated examples with different uniqueness levels were designed, and rotational ambiguity was calculated for each case. In this way, the full implication of partial uniqueness was investigated. Direct visualization of feasible bands is beneficial not only for confirmation of previous rules of uniqueness and partial uniqueness but also for development of new theorems. Copyright © 2013 John Wiley & Sons, Ltd.

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Sufficient conditions for unique solutions within a certain class of curve resolution models

Cited by 28 publications

References 29 publications

Real-life applications of the MULVADO software package for processing DOSY NMR data

Real-life applications of the MULVADO software package for processing DOSY NMR data

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

Visualization and establishment of partial uniqueness and uniqueness rules in parallel factor analysis

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