Orthogonal Projection Approach Applied to Peak Purity Assessment

Sánchez, F. Cuesta; Toft, Jostein; Bogaert, B. van den; Massart, D.L.

doi:10.1021/ac950496g

Cited by 256 publications

(123 citation statements)

References 13 publications

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“…The deviations from the mean final values of the cost function I(Y) are also small for all decompositions indicating that in all cases the global minima were reached. We note that these deviations may be simply due to statistical errors Table 3 which gives comparison with some other MCR methods -IPCA [22], OPA-ALS [46]). …”

Section: Resultsmentioning

confidence: 99%

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

et al. 2006

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We propose a simulated annealing algorithm (called SNICA for "stochastic non-negative independent component analysis") for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The de-mixing is based on a Metropolis type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).

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Section: Resultsmentioning

confidence: 99%

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

et al. 2006

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“…One possible way to do this is by applying PCA on the data set, and taking a look at the number of latent variables with the highest variance. Once the number of likely pathways present in the data is determined, they can be sought using some purity based algorithms [55][56][57][58][59][60][61]. In this work, since we have used the software available at the Multivariate Curve Resolution Homepage [62], the algorithm implemented in Pure function is applied.…”

Section: Multivariate Curve Resolution -Alternating Least Squares (Mcmentioning

confidence: 99%

MCR-ALS on metabolic networks: Obtaining more meaningful pathways

Folch-Fortuny

Tortajada

Prats-Montalbán

et al. 2015

Chemometrics and Intelligent Laboratory Systems

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With the aim of understanding the flux distributions across a metabolic network, i.e. within living cells, Principal Component Analysis (PCA) has been proposed to obtain a set of orthogonal components (pathways) capturing most of the variance in the flux data. The problems with this method are (i) that no additional information can be included in the model, and (ii) that orthogonality imposes a hard constraint, not always reasonably. To overcome these drawbacks, here we propose to use a more flexible approach such as Multivariate Curve Resolution -Alternating Least Squares (MCR-ALS) to obtain this set of biological pathways through the network. By using this method, different constraints can be included in the model, and the same source of variability can be present in different pathways, which is reasonable from a biological standpoint. This work follows a methodology developed for Pichia pastoris cultures grown on different carbon sources, lately presented in [González Martínez et al. 2014].In this paper a different grey modelling approach, which aims to incorporate a priori knowledge through constraints on the modelling algorithms, is applied to the same case of study. The results of both models are compared to show their strengths and weaknesses.

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“…During the optimization, several constraints may be applied depending on the characteristics of the system under study [17,[22][23][24]. Initial estimates can be obtained using chemometric methods such as Evolving Factor Analysis [25], SIMPLISMA [26] or orthogonal projection approach (OPA) [27] to select purest variables that are most dissimilar to each other. Decomposition of the D matrix is accomplished by the iterative optimization of equations (2) and (3) under appropriately chosen constraints:…”

Section: Theoretical Background and Algorithmmentioning

confidence: 99%

Second-order advantage obtained from standard addition first-order instrumental data and multivariate curve resolution-alternating least squares. Calculation of the feasible bands of results

Mohseni

Bahram

Olivieri

2014

Spectrochimica Acta Part A: Molecular and Biomolecular Spectros

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In order to achieve the second-order advantage, two-way data per sample are usually required, e.g., kinetic spectrophotometric data. In this study, instead of monitoring the time evolution of spectra (collecting kinetic-spectrophotometric data) replicate spectra are used to build a spectrophotometric data matrix which is rank deficient. Augmentation of these data with standard addition data [or standard sample(s)] will break the rank deficiency. making the quantification of the analyte of interest possible. These data correspond to the kinetics of all sample constituents being identical when employing second-order kinetic-spectroscopic measurements. The MCR-ALS algorithm has been applied for the resolution and quantitation of the analyte in both simulated and experimental data sets. In order to evaluate the rotational ambiguity in the retrieved solutions, the algorithm MCR-BANDS has been employed. The reliability of the quantitative results significantly depends on the amount of spectral overlap in the spectral region of occurrence of the compound of interest and the remaining constituents. The ability of the proposed algorithm to quantitate the analyte is illustrated both with simulated data systems as well as with binary experimental mixtures.

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Orthogonal Projection Approach Applied to Peak Purity Assessment

Cited by 256 publications

References 13 publications

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

MCR-ALS on metabolic networks: Obtaining more meaningful pathways

Second-order advantage obtained from standard addition first-order instrumental data and multivariate curve resolution-alternating least squares. Calculation of the feasible bands of results

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