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Hyperspectral Raman imaging not only offers spectroscopic fingerprints but also reveals morphological information such as spatial distributions in an analytical sample. However, the spectrum-per-pixel nature of hyperspectral imaging (HSI) results in a vast amount of data. Furthermore, HSI often requires pre- and post-processing steps to extract valuable chemical information. To derive pure spectral signatures and concentration abundance maps of the active spectroscopic compounds, both endmember extraction (EX) and Multivariate Curve Resolution (MCR) techniques are widely employed. The objective of this study is to carry out a systematic investigation based on Raman mapping datasets to highlight the similarities and differences between these two approaches in retrieving pure variables, and ultimately provide guidelines for pure variable extraction. Numerical simulations and Raman mapping experiments on a mixture of pharmaceutical powders and on a layered plastic foil sample were conducted to underscore the distinctions between MCR and EX algorithms (in particular Vertex Component Analysis, VCA) and their outputs. Both methods were found to perform well if the dataset contains pure pixels for each of the individual components. However, in cases where such pure pixels do not exist, only MCR was found to be capable of extracting the pure component spectra., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

Background: Recent interest has been focused on the application of multivariate curve resolution-alternating least-squares (MCR-ALS) to systems involving the measurement of first-order and non-bilinear second-order data. The latter pose important challenges to bilinear decomposition models, due to the phenomenon of rotational ambiguity in the solutions, even under the application of the full set of chemical constraints that is usually employed in MCR-ALS calibration., Results: After the analysis of several simulated and experimental datasets, important conclusions regarding the role of the selectivity patterns in the constituent spectra have been drawn concerning the achievement of the second-order advantage. Theoretical considerations based on the calculation of the areas of feasible solutions helped to support the observations regarding the predictive ability of MCR- ALS in the various datasets., Significance: The understanding of the impact of rotational ambiguity in obtaining the second-order advantage with both first-order and non-bilinear second-order data is of paramount importance in the future development of analytical protocols of complex samples., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Vast evolution in the analytical instruments (e.g. Chemical imaging) makes higher-order data recording more facile. Such sophisticated data acquisition schemes, definitely call for updated data treatment tools. In this way, chemometrics has a decisive role in the analytical chemistry area not only to analyze, but also to expect such data generation possibilities, e.g. combining data coming from instruments with different orders. "Partial trilinearity constraint" is specially planned to cope with differences in bi-and-trilinear models. In this research, we tried to shed light on the accuracy of the mixed multilinear multimodal analysis under partial trilinearity constraint and its conjugation with force-to-zero constraint. For this, several numerical and real experiments are designed by changing the number of components in each block. Finally, some practical guidelines are provided for the analytical chemists., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

A two steps proposal for the purification of immunoglobulin G from human blood plasma is investigated. The first step is precipitation using cold ethanol based on the Cohn method with some modification and the second step is a chromatographic separation by DEAE-Sepharose FF resin as a weak anion exchanger. The presence of interferent in the region3 of chromatographic fractions, which is co-eluted with IgG, restricts the application of the mechanistic chromatography model. Therefore, multivariate cure resolution-alternating least squares (MCR-ALS) as a soft method is employed on measured absorbance data matrix from eluted fractions to recover pure concentration and spectral profiles. Besides, possible solutions for resolved concentration and spectral profiles are investigated. The reaction-dispersive model as a mechanistic hard model for the column is utilized for the evaluation of the ion exchange chromatography. Using a genetic algorithm as a global optimization method, mobile phase modulator (MPM) adsorption model parameters such as β, k des, 0 , and K eq, 0 , were fitted to the concentration profiles from MCR-ALS as 1.96, 2.87×10 -4 m 3 mol -1 s -1 , and 1883, respectively. Furthermore, a new resampling incorporated non-parametric statistics is conducted to assess parameters' uncertainty. Values of 2.00, 1.10×10 -3 m 3 mol -1 s -1 , and 549.80 are estimated median, and values of 0.05, 2.5×10 -3 , and 691.00 are calculated interquartile range (IQR) for β, k des, 0 , and K eq, 0 , respectively. Finally, results show three and two outliers for β and k des, 0 , respectively., Competing Interests: Declaration of Competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

An approach is proposed and illustrated for the joint selection of essential samples and essential variables of a data matrix in the frame of spectral unmixing. These essential features carry the signals required to linearly recover all the information available in the rows and columns of a data set. Working with hyperspectral images, this approach translates into the selection of essential spectral pixels (ESPs) and essential spatial variables (ESVs). This results in a highly-reduced data set, the benefits of which can be minimized computational effort, meticulous data mining, easier model building as well as better problem understanding or interpretation. Working with both simulated and real data, we show that (i) reduction rates of over 99% can be typically obtained, (ii) multivariate curve resolution - alternating least squares (MCR-ALS) can be easily applied on the reduced data sets and (iii) the full distribution maps and spectral profiles can be readily obtained from the reduced profiles and the reduced data sets (without using the full data matrix)., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Smartphones are state-of-the-art devices with several interesting features which make them promising for analytical purposes. After modification to a spectrophotometer (smart spectrophotometer), they can be utilized for the quantitative or qualitative applications. Although smartphones have widely been applied for sensing∖biosensing purposes, the error structure/type of their outputs remained unexplored. Error structure information values the objects/channels in a given data set and variables have the same importance when the noise has identical independent distribution (i.i.d). Otherwise, error structure weights them for further data analysis. In this contribution, a smartphone-based spectrophotometer was constructed integrating simple optical elements-a tungsten lamp as source and a piece of digital versatile disc (DVD) as a reflecting diffraction grating to investigate the error sources of the smartphone-spectrophotometer. For this purpose, error covariance matrices (ECMs) were calculated using a series of replication capturing error information. Afterwards, PCA and MCR-ALS were employed for the decomposition of the ECMs and resolved profiles were translated to the error types. Finally, proportional error as a heteroscedastic noise was highlighted as the most important source of variation in the error structure of the smartphone-based spectrophotometer., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Bilinear decomposition of an augmented data matrix is usually complicated by the phenomenon of rotational ambiguity. If the latter is significant, quantitative and qualitative information of the recovered profiles may be less useful. Although constraints can reduce the extent of feasible regions and the degree of rotational ambiguity, the estimation of initial parameters to start the decomposition is an important phase in multivariate curve resolution-alternating least-squares (MCR-ALS) studies. Dealing with a bilinear decomposition of an augmented data matrix where rotational ambiguity persists, the question remains whether it is possible to still develop a successful calibration protocol. Indeed, literature reports indicate that various analytical systems have been experimentally developed, in which substantial rotational ambiguity exists, yet the experimental results confirmed that accurate analyte quantitation was possible. In this research, we further investigate on the effect of the initialization step for a two-component second-order multivariate calibration with the extended bilinear model. It is shown that the selection strategy based on the so-called purest variables can be helpful in achieving a correct profile resolution, depending on which data direction it is applied. Finally, some data-driven guidelines for analytical chemists are suggested, to identify the potential degree of rotational ambiguity and the correct choice of the initialization strategy., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Although many efforts have been directed to the development of approximation methods for determining the extent of feasible regions in two- and three-way data sets; analytical determination (i.e. using only finite-step direct calculation(s) instead of the less exact numerical ones) of feasible regions in three-way arrays has remained unexplored. In this contribution, an analytical solution of trilinear decomposition is introduced which can be considered as a new direct method for the resolution of three-way two-component systems. The proposed analytical calculation method is applied to the full rank three-way data array and arrays with rank overlap (a type of rank deficiency) loadings in a mode. Close inspections of the analytically calculated feasible regions of rank deficient cases help us to make clearer the information gathered from multi-way problems frequently emerged in physics, chemistry, biology, agricultural, environmental and clinical sciences, etc. These examinations can also help to answer, e.g., the following practical question: "Is two-component three-way data with proportional loading in a mode actually a three-way data array?" By the aid of the additional information resulted from the investigated feasible regions of two-component three-way data arrays with proportional profile in a mode, reasons for the inadequacy of the seemingly trilinear data treatment methods published in the literature (e.g., U-PLS/RBL-LD that was used for extraction of quantitative and qualitative information reported by Olivieri et al. (Anal. Chem. 82 (2010) 4510-4519)) could be completely understood., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general. Our proposed detection tool is restricted to three-component systems because of the visual limitations of the Borgen plot, but the theorem is universal for systems with more than three components. A recently published experimental four-component system is used for illustrating this theorem in the case of systems with more than three components., (Copyright © 2014 Elsevier B.V. All rights reserved.)

Unambiguous recovery of profiles is a distinguishable advantage of Parallel Factor Analysis (PARAFAC) as a trilinear model and has made it a promising exploratory tool for data analysis. Linear dependency in profiles destroys trilinearity and will increase ambiguity in the curve resolution of three-way data sets. PARAFAC uniqueness deteriorates totally or partially in data sets with linearly dependent loadings. Exploiting a reliable method for determination and direct visualization of feasible bands in the PARAFAC model can be helpful not only in full characterization of uniqueness conditions but also in the investigation of the effects of constraints on the PARAFAC feasible solutions. The purpose of this paper is twofold. First, the calculation of rotational ambiguity in the PARAFAC model extends to three components system. The principle behind the algorithm is described in detail and tested for simulated and real data sets. Completely general and thoroughly investigated results are presented for the three component cases. Secondly, the effects of selective regions in the profiles on the resolution of systems that suffered from the rank deficiency problem, due to rank overlap, are emphasized. In the case of two-way data sets the effect of selectivity constraint on the unique recovery of profiles was investigated and applied. However, to our knowledge, in this report, for the first time, the effect of the presence of selective windows in the profiles, on the unique resolution of three-way data sets has been systematically investigated., (Copyright © 2013 Elsevier B.V. All rights reserved.)