Multivariate Curve Resolution (MCR) covers a wide span of algorithms designed to tackle the mixture analysis problem by expressing the original data through a bilinear model of pure component ...meaningful contributions. Since the seminal work by Lawton and Sylvestre in 1971, MCR methods are dynamically evolving to adapt to a wealth of diverse and demanding scientific scenarios. To do so, essential concepts, such as basic constraints, have been revisited and new modeling tasks, mathematical properties and domain-specific information have been incorporated; the initial underlying bilinear model has evolved into a flexible framework where hybrid bilinear/multilinear models can coexist, the regular data structures have undergone a turn of the screw and incomplete multisets and matrix and tensor combinations can be now analyzed. Back to the fundamentals, the theoretical core of the MCR methodology is deeply understood due to the thorough studies about the ambiguity phenomenon. The adaptation of the method to new analytical measurements and scientific domains is continuous. At this point of the story, MCR can be considered a mature yet lively methodology, where many steps forward can still be taken.
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•The main advances of Multivariate Curve Resolution from 1971 to 2020 are reviewed.•New constraints based on mathematical or natural profile properties are described.•New challenging data structures used in MCR are presented.•Main advances in estimating and understanding the ambiguity phenomenon are addressed.•New application domains, such as -omics, imaging or multidimensional chromatography are mentioned.
The extension of Multivariate Curve Resolution‐Alternating Least Squares (MCR‐ALS) to the analysis of multiway data using the multilinearity constraint is described in detail as one step forward of ...previous implementations of the trilinearity and quadrilinearity constraints for the analysis of three‐ and four‐way data sets, respectively. As in previous cases, the implementation of the multilinear model for multiway data sets is done algorithmically, within the frame of the alternating least squares (ALS) optimization in the MCR‐ALS method. This implementation is tested using multiway data sets of different complexity, and the obtained results have confirmed the adequacy of the proposed approach. Special advantages of the proposed methodology are that it allows for the implementation of the constraint separately for the different components in their different modes and that it also allows for the introduction of different levels of complexity of the multilinear model, including mixed multilinear models. These two features are especially relevant because they are not present in most of the most used multiway data analysis methods at present.
The extension of Multivariate Curve Resolution‐Alternating Least Squares (MCR‐ALS) to the analysis of multiway data using the multilinearity constraint is described in detail as one step forward of previous implementations of the trilinearity and quadrilinearity constraints for the analysis of threeand four‐way data sets respectively. This implementation is tested using multiway data sets of different complexity, and the obtained results have confirmed the adequacy of the proposed approach. Special advantages of the proposed methodology are that it allows for the implementation of the constraint separately for the different components in their different modes and that it also allows for the introduction of different levels of complexity of the multilinear model, including mixed multilinear models. These two features are especially relevant because they are not present in most of the most used multiway data analysis methods at present.
An updated version of the graphical user-friendly interface related to the Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) algorithm is presented. This GUI works under MATLAB® ...environment and includes recently published advances of this algorithm linked to the implementation of additional constraints, such as kinetic hard-modeling and correlation (calibration), as well as constraints linked to model structure for multiset and multi-way data analysis, such as the possibility to use fully or partially multilinear models (trilinear or quadrilinear) to describe the data set.
In addition, a step has been included to allow the preliminary subspace maximum likelihood projection to decrease noise propagation effects in case of large non-homoscedastic uncertainties, and the possibility of direct selection of number of components and of initial estimates.
Finally, a number of options to present and handle the output information have been added, such as the display of data fitting evolution, improvement in the display of loading profiles in different modes for multi-way data, refolding MCR scores into 2D distribution maps for hyperspectral images and the internal connection to the MCR-Bands GUI, previously designed for the assessment of the extent and location of ambiguities in the MCR resolved profiles. Different examples of use of this updated interface are given in this work.
•A new version of the MCR-ALS graphical user-friendly interface is presented.•New constraints are available: kinetic hard-modeling, calibration, multilinear, etc.•Several output options have been added to facilitate interpretation of the results.•Examples from different fields of application are discussed.
Raman and Fourier transform IR (FTIR) microspectroscopic images of biological material (tissue sections) contain detailed information about their chemical composition. The challenge lies in ...identifying changes in chemical composition, as well as locating and assigning these changes to different conditions (pathology, anatomy, environmental or genetic factors). Multivariate data analysis techniques are ideal for decrypting such information from the data. This protocol provides a user-friendly pipeline and graphical user interface (GUI) for data pre-processing and unmixing of pixel spectra into their contributing pure components by multivariate curve resolution-alternating least squares (MCR-ALS) analysis. The analysis considers the full spectral profile in order to identify the chemical compounds and to visualize their distribution across the sample to categorize chemically distinct areas. Results are rapidly achieved (usually <30-60 min per image), and they are easy to interpret and evaluate both in terms of chemistry and biology, making the method generally more powerful than principal component analysis (PCA) or heat maps of single-band intensities. In addition, chemical and biological evaluation of the results by means of reference matching and segmentation maps (based on k-means clustering) is possible.
The analysis of LC-MS metabolomic datasets appears to be a challenging task in a wide range of disciplines since it demands the highly extensive processing of a vast amount of data. Different LC-MS ...data analysis packages have been developed in the last few years to facilitate this analysis. However, most of these strategies involve chromatographic alignment and peak shaping and often associate each "feature" (i.e., chromatographic peak) with a unique m/z measurement. Thus, the development of an alternative data analysis strategy that is applicable to most types of MS datasets and properly addresses these issues is still a challenge in the metabolomics field.
Here, we present an alternative approach called ROIMCR to: i) filter and compress massive LC-MS datasets while transforming their original structure into a data matrix of features without losing relevant information through the search of regions of interest (ROIs) in the m/z domain and ii) resolve compressed data to identify their contributing pure components without previous alignment or peak shaping by applying a Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis. In this study, the basics of the ROIMCR method are presented in detail and a detailed description of its implementation is also provided. Data were analyzed using the MATLAB (The MathWorks, Inc., www.mathworks.com ) programming and computing environment. The application of the ROIMCR methodology is described in detail, with an example of LC-MS data generated in a lipidomic study and with other examples of recent applications.
The methodology presented here combines the benefits of data filtering and compression based on the searching of ROI features, without the loss of spectral accuracy. The method has the benefits of the application of the powerful MCR-ALS data resolution method without the necessity of performing chromatographic peak alignment or modelling. The presented method is a powerful alternative to other existing data analysis approaches that do not use the MCR-ALS method to resolve LC-MS data. The ROIMCR method also represents an improved strategy compared to the direct applications of the MCR-ALS method that use less-powerful data compression strategies such as binning and windowing. Overall, the strategy presented here confirms the usefulness of the ROIMCR chemometrics method for analyzing LC-MS untargeted metabolomics data.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
This article is a tutorial that focuses on the main aspects to be considered when applying Multivariate Curve Resolution to analyze multicomponent systems, particularly when the Multivariate Curve ...Resolution-Alternating Least Squares (MCR-ALS) algorithm is used. These aspects include general MCR comments on the potential fields of application and construction of data structures and details linked to each of the steps in the application workflow of the MCR-ALS algorithm ( e.g. , selection of initial estimates, choice and application of constraints, quality parameters of models and assessment of ambiguity,…). Two examples with downloadable data sets are shown for orientation on the practical use of this methodology.
Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) can analyze three-way data under the assumption of a trilinear model using the trilinearity constraint. However, the rigid ...application of this constraint can produce unrealistic solutions in practice due to the inadequacy of the analyzed data to the characteristics and requirements of the trilinear model. Different methods for the relaxation of the trilinear model data requirements have been proposed, like in the PARAFAC2 and in the direct non-trilinear decomposition (DNTD) methods. In this work, the trilinearity constraint of MCR-ALS is adapted to different data scenarios where the profiles of all or some of the components of the system are shifted (not equally synchronized) or even change their shape among different slices in one of their data modes. This adaptation is especially useful in gas and liquid chromatography (GC and LC) and in Flow Injection Analysis (FIA) with multivariate spectroscopic detection. In a first data example, a synthetic LC-DAD dataset is built to investigate the possibilities of the proposed method to handle systematic changes (shifts) in the retention times of the elution profiles and the results are compared with those obtained using alternative methods like ATLD, PARAFAC, PARAFAC2 and DNTD. In a second data example, multiple wine samples were simultaneously analyzed by GC-MS where elution profiles presented large deviations (shifts) in their peak retention times, although they still preserve the same peak shape. Different modelling scenarios are tested and the results are also compared. Finally, in the third example, sample mixtures of acid compounds were analyzed by FIA under a pH gradient and monitored by UV spectroscopy and also examined by different chemometric methods using a different number of components. In this case, however, the departure of the trilinear model comes from the acid base speciation of the system depending on the pH more than from the shifting of the FIA diffusion profiles.
•Data analysis is the “bottleneck” of metabolomic LC-MS studies.•Huge amounts of data are produced by LC-MS metabolomics.•LC-MS data analysis strategies vary according to the type of metabolomic ...study: targeted or untargeted.•Numerous data analysis methodologies exist with different capabilities.•This review shows distinct data analysis strategies for LC-MS metabolomic studies.
Data analysis is a very challenging task in LC-MS metabolomic studies. The use of powerful analytical techniques (e.g., high-resolution mass spectrometry) provides high-dimensional data, often with noisy and collinear structures. Such amount of information-rich mass spectrometry data requires extensive processing in order to handle metabolomic data sets appropriately and to further assess sample classification/discrimination and biomarker discovery.
This review shows the steps involved in the data analysis workflow for both targeted and untargeted metabolomic studies. Especial attention is focused on the distinct methodologies that have been developed in the last decade for the untargeted case. Furthermore, some powerful and recent alternatives based on the use of chemometric tools will also be discussed. In general terms, this review helps researchers to critically explore the distinct alternatives for LC-MS metabolomic data analysis to better choose the most appropriate for their case study.
The presence of rotation ambiguities and unique solutions in Multivariate Curve Resolution (MCR) chemometric methods is discussed in detail. Using recently proposed graphical approaches to display ...the bands and areas of feasible solutions in a subspace of reduced dimensions, the results obtained by different MCR methods are compared. These results show that in the presence of rotation ambiguities and under a particular set of constraints, the solutions obtained by the different MCR methods can differ among them and also from the true solution depending on initial estimates and on the applied algorithm. In absence of rotational ambiguities, all MCR methods should give the same unique solution which should be equal to the true one. Many of the MCR methods proposed in the literature like MCR-ALS, RFA, MCR-FMIN, or MCR-BANDS are confirmed to give a valid solution within the band or area of feasible solutions. On the contrary, and according to the results of this study, in its present implementation, the minimum volume simplex analysis, MVSA method can give unfeasible solutions when resolving bilinear data systems with more than two components, because it only applies non-negativity constraints to concentration profiles and not to spectral profiles.
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