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Spectroscopic measurements can show distorted spectral shapes arising from a mixture of absorbing and scattering contributions. These distortions (or baselines) often manifest themselves as non-constant offsets or low-frequency oscillations. As a result, these baselines can adversely affect analytical and quantitative results. Baseline correction is an umbrella term where one applies pre-processing methods to obtain baseline spectra (the unwanted distortions) and then remove the distortions by differencing. However, current state-of-the art baseline correction methods do not utilize analyte concentrations even if they are available, or even if they contribute significantly to the observed spectral variability. We modify a class of state-of-the-art methods (penalized baseline correction) that easily admit the incorporation of a priori analyte concentrations such that predictions can be enhanced. This modified approach will be deemed supervised and penalized baseline correction (SPBC). Performance will be assessed on two near infrared data sets across both classical penalized baseline correction methods (without analyte information) and modified penalized baseline correction methods (leveraging analyte information). There are cases of SPBC that provide useful baseline-corrected signals such that they outperform state-of-the-art penalized baseline correction algorithms such as AIRPLS. In particular, we observe that performance is conditional on the correlation between separate analytes: the analyte used for baseline correlation and the analyte used for prediction—the greater the correlation between the analyte used for baseline correlation and the analyte used for prediction, the better the prediction performance. • Exploit references (i.e., analyte concentrations) in baseline correction are novel. • Penalized baseline correction methods can easily accommodate reference measurements. • Analyte concentrations used for baseline correction and analyte concentrations used for prediction can be different. • Increased correlation between various analytes improves performance. [ABSTRACT FROM AUTHOR]

Few-shot learning poses a critical challenge due to the deviation problem caused by the scarcity of available samples. In this work, we aim to address deviations in both feature representations and prototypes. To achieve this, we propose a cross-modal de-deviation framework that leverages class semantic information to provide robust prior knowledge for the samples. This framework begins with a visual-to-semantic autoencoder trained on the labeled samples to predict semantic features for the unlabeled samples. Then, we devise a binary linear programming model to match the initial prototypes with the cluster centers of the unlabeled samples. To circumvent potential mismatches between the cluster centers and the initial prototypes, we perform the label assignment process in the semantic space by transforming the cluster centers into semantic representations and utilizing the class ground truth semantic features as reference points. Moreover, we model a linear classifier with the concatenation of the refined prototypes and the class ground truth semantic features serving as the initial weights. Then we propose a novel optimization strategy based on the alternating least squares (ALS) model. From the ALS model, we can derive two closed-form solutions regarding to the features and weights, facilitating alternative optimization of them. Extensive experiments conducted on few-shot learning benchmarks demonstrate the competitive advantages of our CMDD method over the state-of-the-art approaches, confirming its effectiveness in reducing deviation. The code is available at: https://github.com/pmhDL/CMDD.git. • Our CMDD method reduces prototype deviation through cross-modal label assignment, mitigating the risk of collapsing multiple clusters into one class and minimizing the impact of limited labeled samples on the refined prototypes. • An alternative optimization strategy based on the alternating least squares model is explored to optimize the features and classifier's weights, effectively promoting mutual enhancement between them. • Our CMDD method competes well with state-of-the-art approaches, demonstrated through comprehensive experiments and ablation studies on four few-shot benchmarks. [ABSTRACT FROM AUTHOR]

Abstract This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank 23 decompositions for the 3 × 3 matrix multiplication tensor M 〈 3 〉. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of M 〈 n 〉 for larger n. [ABSTRACT FROM AUTHOR]

Abstract The regularization method could deal with the swamp effect of alternating least squares (ALS) algorithms for tensor decomposition. Usually, the regularization term is a norm of the difference between the solution and the current iterate. In this paper, we show that the norm could be weakened to a seminorm, so the selection of the regularization term could be more flexible. To overcome the swamp effect and avoid the drawback that the Hessian of the subproblem may get close to singular in the iterative process, we propose a seminorm regularized ALS algorithm for solving the canonical tensor decomposition. Moreover, in the new algorithm, we introduce a novel extrapolation in the update of each mode factor which makes an immediate impression on the update of subsequent ones. By assuming the boundness of the infinite sequence of iterates generated by the new algorithm, we establish the global convergence and the (weakly) linear convergence rate of the sequence of iterates Numerical experiments on synthetic and real-world problems illustrate that the new method is efficient and promising. [ABSTRACT FROM AUTHOR]

Gaussian apodization factor analysis (GAFA) has been developed as an enhanced algorithm to assess the peak purity of the two-dimensional data, by weighting the fixed-size moving window via Gaussian formula. In GAFA method, submatrices are extracted by Gaussian apodization moving window. Therefore, each submatrix mainly characterizes the spectrum and by performing factor analysis on this Gaussian weighted submatrix, the number of principal components for each evaluated spectrum, is determined. This precise and quick determination of a rank map is successfully used for extract pure components from hyphenated chromatographic data. An algorithm based on GAFA was applied to resolve different types of overlapped simulated and real complex data of GC–MS. This algorithm finds spectra of pure component with GAFA one by one and eliminates obtained components from a data matrix and search for next pure component spectra until all the components are determined. [ABSTRACT FROM AUTHOR]

The analysis of mixtures is a routine task in the analytical chemistry area as well as in other research fields. The objective is to identify, quantify, and interpret the chemical components of the mixtures. Various bilinear factor decomposition methods, including MCR-ALS, NMFand BNFA, have been proposed to solve this problem. However, there is little knowledge about their comparative performance in terms of different factors, such as solution reliability, calculation speed, convergence, flexibility in constraint implementation, and ease of results interpretation. To address these issues, this work aims to compare these methods using data examples from data simulations, environmental source apportionment studies, and chromatographic analysis of chemical mixtures. Through this comparison, we hope to gain insights into the strengths and weaknesses of each method and provide recommendations for researchers working in this field. This comprehensive comparison will help researchers choose the appropriate method for their specific analysis needs, ultimately leading to more accurate and efficient analysis. • Various bilinear factor decomposition, including MCR-ALS, NMF, and BNFA are compared. • Bilinear non-negative factor decompositions are widely used in various scientific fields. • MCR-ALS convergence is guaranteed and further constraints can be easily implemented. • Different resolution algorithms drive solutions to a different part of the feasible region. [ABSTRACT FROM AUTHOR]

Hyperspectral imaging acquires up to several hundreds of narrow and adjacent spectral band images simultaneously. However, since the dimension of the hyperspectral imaging data, which typically forms a third order tensor, is increased in proportion to the size of spatial and the spectral information at the same time, the higher order singular value decomposition (HOSVD) is appropriate to reduce its dimension. One of the simplest and most accurate approaches for computing the HOSVD is higher order orthogonal iteration (HOOI), which computes the factor matrices from the unfolding matrices of the given tensor by using singular value decomposition alternatively until convergence is achieved. However, because of its expensive computational complexity, we propose a faster algorithm to compute the HOSVD even though the output shows no meaningful difference from that obtained by HOOI. Specifically instead of computing the factor matrix from the updated tensor in every iteration along each mode, we reuse the intermediate result after updating one factor matrix to modify the others in a single iteration. Numerical experiments reveal that the proposed algorithm computes the dimension-reduced hyperspectral imaging much faster than HOOI with fewer outer iterations. Moreover, the difference in accuracy between the proposed algorithm and HOOI is negligible. [ABSTRACT FROM AUTHOR]

Forty-eight crude oil samples collected from different reservoirs in the Tahe oilfield of the Tarim Basin were investigated. Based on geochemical characteristics, it is concluded that the oil samples originated from multiple marine source rocks deposited in various sedimentary environments and subsequently altered by different levels of thermal maturation. These mixtures were de-convoluted to three endmember oils (EM1, EM2 and EM3) by alternating least squares regression using 38 concentration parameters. EM1 is the minimum contributor with an average of 13%, while EM2 and EM3 are the main contributors to the mixtures with averages of 52% and 35%, respectively. EM1 oil originated from Cambrian–Lower Ordovician source rocks in the early to peak oil window and subsequently experienced two phases of mixing and biodegradation. EM2 and EM3 oils originated from Middle–Upper Ordovician source rocks, but EM2 was generated at lower thermal maturity than EM3. The EM2 oil underwent two phases of mixing and one stage biodegradation, while the EM3 oil mixed with previous existing mixtures in the reservoirs. The final mixtures that might be affected by secondary processes, such as evaporative fractionation, are currently produced from the Tahe oilfield. The general orientation of oil filling was from south to north and east to west based on variations in the relative contributions of EMs, and the total concentrations of dibenzothiophenes and dibenzofurans in the oils. Considering the histories of sedimentary tectonic evolution, hydrocarbon generation and expulsion, and the de-convolution results, a model of three stages of oil charge and two phases of mixing and biodegradation was established for the Tahe oilfield oils. [ABSTRACT FROM AUTHOR]

The paper presents a new analytical tool to solve the classical photogrammetric bundle block adjustment. The analytical model is based on the generalized extension of the anisotropic row-scaling Procrustes analysis, that has been recently proposed by the same authors to solve the image exterior orientation problem. The main advantage of the method is given by the fact that the problem solution does not require any approximate value of the unknown parameters, nor any linearization procedure. Moreover, the algorithm is exceedingly simple to describe and easy to implement. Empirical results indicate that a zero-information initialization of the iterative relaxation procedure leads almost always to the correct final least squares solution. Experiments confirm the accuracy of the proposed method, when compared to the results obtained by applying a classical photogrammetric bundle block adjustment. [ABSTRACT FROM AUTHOR]

In this work, Raman hyperspectral images and multivariate curve resolution-alternating least squares (MCR-ALS) are used to study the distribution of actives and excipients within a pharmaceutical drug product. This article is mainly focused on the distribution of a low dose constituent. Different approaches are compared, using initially filtered or non-filtered data, or using a column-wise augmented dataset before starting the MCR-ALS iterative process including appended information on the low dose component. In the studied formulation, magnesium stearate is used as a lubricant to improve powder flowability. With a theoretical concentration of 0.5% (w/w) in the drug product, the spectral variance contained in the data is weak. By using a principal component analysis (PCA) filtered dataset as a first step of the MCR-ALS approach, the lubricant information is lost in the non-explained variance and its associated distribution in the tablet cannot be highlighted. A sufficient number of components to generate the PCA noise-filtered matrix has to be used in order to keep the lubricant variability within the data set analyzed or, otherwise, work with the raw non-filtered data. Different models are built using an increasing number of components to perform the PCA reduction. It is shown that the magnesium stearate information can be extracted from a PCA model using a minimum of 20 components. In the last part, a column-wise augmented matrix, including a reference spectrum of the lubricant, is used before starting MCR-ALS process. PCA reduction is performed on the augmented matrix, so the magnesium stearate contribution is included within the MCR-ALS calculations. By using an appropriate PCA reduction, with a sufficient number of components, or by using an augmented dataset including appended information on the low dose component, the distribution of the two actives, the two main excipients and the low dose lubricant are correctly recovered. [ABSTRACT FROM AUTHOR]

The PARAFAC method is an approach to decompose multidimensional arrays into component matrices for a given number of components. The most common way for calculating the decomposition is the alternating least squares method (ALS). Many other algorithms are modifications of ALS, including algorithms utilizing line search, enhanced line search or Tikhonov regularization. These algorithms and a new one, combining line search and Tikhonov regularization, are discussed in this paper. It is demonstrated that the new algorithm combines fast computation and successful handling of ill-conditioned problems, like given in the case of bottlenecks and swamps. Another point discussed is the application of compression for improving the algorithms considered. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the application of the Multivariate Curve Resolution Alternating Least Squares method (MCR-ALS) to incomplete data multisets is explored. The experimental incomplete data multiset studied in this work is taken from a previous multiannual atmospheric monitoring study of the changes of ozone and nitrogen oxide concentrations in an air quality sampling station located in the city of Barcelona, in which some of the individual data sets were missing. Based on the preliminary results obtained in this study, new data multisets, complete and incomplete, with different levels of noise were simulated and analysed by a new variant of the MCR-ALS method which optimises a combined error function including all possible complete data subsets derived from the original incomplete data multiset. Conclusions are drawn about the effects of data completeness on the results obtained for different noise levels and on the viability of trilinear models. [Copyright &y& Elsevier]

Abstract: We show that the problems of approximating tensors and multivariate functions as a sums of (tensor) products of vectors/functions can be considered in a unified framework, thus exposing their common multilinear structure. We study the alternating least squares algorithm within this framework from the orthogonal projection and gradient perspectives. We then use these perspectives to study its convergence behavior with and without regularization. Finally, we formulate the infinite dimensional version of this problem and an algorithm to compute in that context. [Copyright &y& Elsevier]

Abstract: Determination of the compounds that are present in molecular clouds is carried out from the study of the infrared spectrum of astrophysical ices. This analysis plays a fundamental role in the prediction of the future evolution of the cloud under study. The process is simulated in the laboratory under similar conditions of thermal and energetic processing, recording the infrared absorption spectrum of the resultant ice. The spectrum of each ice can be modeled as the linear instantaneous superposition of the spectrum of the different compounds, so a Source Separation approach is appropriate. We propose the use of Alternating Least Squares and a Regularized version to identify the molecules that are present in the ice mixtures. Since the spectra and abundances are non-negative, a non-negativity constraint can be applied to obtain solutions with physical meaning. We perform several simulations of synthetic and real mixtures of ices in order to compare both solutions and to show how the proposed approach provides an efficient way to recover underlying spectral patterns that are physically meaningful. [Copyright &y& Elsevier]

Abstract: A comparison of the results obtained using three algorithms, Multivariate Curve Resolution Alternating Least Squares (MCR-ALS), Multivariate Curve Resolution Weighted Alternating Least Squares (MCR-WALS) and Maximum Likelihood Principal Component Analysis Multivariate Curve Resolution Alternating Least Squares (MLPCA-MCR-ALS), is presented. The three approaches are applied to the analysis of a simulated environmental data set with error structures of different types and sizes. Special attention is paid to the case of highly heteroscedastic correlated noise. In all cases, the results show that the solutions provided by MLPCA-MCR-ALS are practically identical to those obtained by MCR-WALS. [Copyright &y& Elsevier]

Abstract: A problem with self-modeling mixture analysis solutions is the range of solutions that is generally possible. The range of solutions goes from those with high contrast spectra and low contrast contributions/images to solutions with high contrast contributions/images and low contrast spectra. The term contrast is a measure for dissimilarity, which results in simpler spectra or images. Because of their simplicity, the extremes of this solution range often have clear advantages for the interpretation of the data. Previously, an angle modification in alternating least squares self-modeling mixture analysis has been shown as a method of identifying these extremes. The utility of this method of this utility will be demonstrated in this paper with : autofluorescence spectroscopy microscopy images of lung cells; secondary ion mass spectrometry (SIMS) analysis of a sample obtained by laser activation modification of semiconductor surfaces (LAMSS) and energy dispersive X-ray fluorescence (EDXRF) of a granite sample. [Copyright &y& Elsevier]

Abstract: There has been a tremendous increase in research on comprehensive two dimensional LC (LC×LC); however, to date, the central analytical issue, quantification, has received only minimal attention. It is vital to the further development of LC×LC that a greater understanding of the specific factors affecting peak quantification in LC×LC be attained. This work focuses on the following factors: data complexity, retention time shifting, dynamic range issues, chromatographic and spectral peak overlap and difficulties related to background signal removal. The above mentioned factors that affect peak quantification are investigated using fourteen replicate analyses of a urine sample, representing the effects of such factors when analyzing samples in complex matrices. We demonstrate that quantification of LC×LC data is improved following implementation of chemometric techniques that minimized the deleterious effects on quantification due to chromatographically overlapped peaks, retention time shifting and background signal interference. The chemometrically resolved data shows a 2.5-fold increase in precision of quantification over the quantification of the raw data. It is also demonstrated that the method quantifies sixteen peaks that were not visually evident prior to chemometric analysis. The purpose of this paper is to determine the impact of these issues on the effectiveness of LC×LC as a technique for the quantitative analysis of complex samples. [Copyright &y& Elsevier]

Abstract: Parallel factor analysis (PARAFAC) is a tensor (multiway array) factorization method which allows to find hidden factors (component matrices) from a multidimensional data. Most of the existing algorithms for the PARAFAC, especially the alternating least squares (ALS) algorithm need to compute Khatri–Rao products of tall factors and multiplication of large matrices, and due to this require high computational cost and large memory and are not suitable for very large-scale-problems. Hence, PARAFAC for large-scale data tensors is still a challenging problem. In this paper, we propose a new approach based on a modified ALS algorithm which computes Hadamard products, instead Khatri–Rao products, and employs relatively small matrices. The new algorithms are able to process extremely large-scale tensors with billions of entries. Extensive experiments confirm the validity and high performance of the developed algorithm in comparison with other well-known algorithms. [Copyright &y& Elsevier]

Abstract: Two-dimensional liquid chromatography (LC×LC) is quickly becoming an important technique for the analysis of complex samples, owing largely to the relatively high peak capacities attainable by this analytical technique. With the increase in the complexity of the sample comes a corresponding increase in the complexity of the collected data. Thus the need for chemometric methods capable of resolving and quantifying such data is ever more urgent in order to obtain the maximum information available from the data. To this end, we have developed a chemometric method that combines iterative key set factor analysis and multivariate curve resolution-alternating least squares analysis with a spectral selectivity constraint that is shown to be capable of resolving chromatographically rank deficient, non-multilinear data. (spectrally rank deficient compounds can only be quantified if the peaks having the same spectra are chromatographically resolved). Over 50 chromatographic peaks were found in a relatively small section of a LC×LC-diode array data set of replicate urine samples (a four-way data set) using the developed method. The relative concentrations for 34 of the 50 peaks were determined with % RSD values ranging from 0.09% to 16%. [Copyright &y& Elsevier]

Abstract: Despite significant recent interest in the identification of electrically stimulated muscle models, current methods are based on underlying models and identification techniques that make them unsuitable for use with subjects who have incomplete paralysis. One consequence of this is that very few model-based controllers have been used in clinical trials. Motivated by one case where a model-based controller has been applied to the upper limb of stroke patients, and the modelling limitations that were encountered, this paper first undertakes a review of existing modelling techniques with particular emphasis on their limitations. A Hammerstein structure, already known in this area, is then selected, and a suitable identification procedure and set of excitation inputs are developed to address these short-comings. The technique that is proposed to obtain the model parameters from measured data is a combination of two iterative schemes: the first of these has rapid convergence and is based on alternating least squares, and the second is a more complex method to further improve accuracy. Finally, experimental results are used to assess the efficacy of the overall approach. [Copyright &y& Elsevier]

Abstract: A direct spectrophotometric method for the determination of three artificial colors – amaranth, sunset yellow FCF and tartrazine – in beverages samples is proposed. The spectra were recorded between 359 and 600nm. The spectra of the samples (just filtrated), pure dyes (concentrations ranged between 0.01 and 1.8mgL−1 for amaranth, 0.08 and 4.4mgL−1 for sunset yellow and 0.04 and 1.8mgL−1 for tartrazine) and synthetic mixtures were disposed in a column-wise augmented data matrix. This kind of data structure, analyzed by multivariate curve resolution-alternating least squares (MCR-ALS) makes it possible to exploit the so called ‘second order advantage’. MCR-ALS algorithm was applied to the experimental data under the non-negativity and equality constraints. As a result, the concentration of each dye in the samples and their corresponding pure spectra were obtained. The results were validated using internal reference materials and no significant differences were found (α =5%) between the reference values and the ones obtained with the proposed method. The second order advantage made it possible to obtain unbiased results even in the presence of interferences. [Copyright &y& Elsevier]

Abstract: The aza-Michael reaction, a variation of the Michael reaction in which an amine acts as the nucleophile, permits the synthesis of sophisticated macromolecular structures with potential use in many applications such as drug delivery systems, high performance composites and coatings. The aza-Michael product can be affected by a retro-Mannich-type fragmentation. A way of determining the reactions that are taking place and evaluate the quantitative evolution of the chemical species involved in the reactions is presented. The aza-Michael reaction between a modified fatty acid ester with α,β-unsaturated ketone groups (enone containing methyl oleate (eno-MO)) and aniline (1:1) was studied isothermally at 95°C and monitored in situ by near-infrared spectroscopy (NIR). The number of reactions involved in the system was determined analyzing the rank matrix of NIR spectra data recorded during the reaction. Singular value decomposition (SVD) and evolving factor analysis (EFA) adapted to analyze full rank augmented data matrices have been used. In the experimental conditions, we found that the resulting aza-Michael adduct undergoes a retro-Mannich-type fragmentation, but the final products of this reaction were present in negligible amounts. This was confirmed by recording the 1H NMR spectra of the final product. Applying multivariate curve resolution-alternating least squares (MCR-ALS) to the NIR spectra data obtained during the reaction, it has been possible to obtain the concentration values of the species involved in the aza-Michael reaction. The performance of the model was evaluated by two parameters: ALS lack of fit (lof=1.31%) and explained variance (R 2 =99.92%). Also, the recovered spectra were compared with the experimentally recorded spectra for the reagents (aniline and eno-MO) and the correlation coefficients (r) were 0.9997 for the aniline and 0.9578 for the eno-MO. [Copyright &y& Elsevier]

Abstract: A comprehensive study of the applicability of multivariate curve resolution (MCR) methods to series of T2-relaxation filtered 1H NMR spectra of a cross-linked polymer network is presented. A collection of Hahn-echo NMR spectra is obtained at different echo times, yielding two-way data. In this study the applicability of two different types of orthogonal-projection approach (OPA1 and OPA2) (column-wise and row-wise) were tested. Four different strategies of alternating least squares methods were also examined (ALS1, ALS2, ALS3 and ALS4). These strategies differed on the order of measurement for which the constraints were applied in the final output, and the way in which SSR was calculated to monitor for convergence. In the spectral order of measurement, a non-negativity constraint was imposed, whereas in the time order of measurement, the signal was forced to follow an exponential decay. This yielded up to eight MCR configurations, giving different results. For solid-state NMR, the dissimilarity in NMR profiles is significantly lower than the dissimilarity in signal decays, and therefore OPA2 performed better. A final output with a constrained solution in relaxation time was preferred (instead of a constrained solution in NMR spectra) for practical purposes. Differences between the solutions given from the two ALS configurations can be interpreted as a sign of lack of fit. [Copyright &y& Elsevier]

Abstract: A novel electrochemical method, based on differential pulse voltammetry (DPV) in a rotating Au-disk electrode, is proposed to study Hg2+ binding with various ligands. It consisted in applying a previous deposition potential that allowed the adsorption of Hg2+ ions and/or their complexes on Au surface, followed by a cathodic potential scan. In that way, Hg2+-reduction signals, for both free and complexed Hg2+, can be observed. The classical DPV scheme, without any preconcentration step, did not yield reproducible and reliable results. The method has been applied to the complexation of Hg2+ with diethylenetriaminepentaacetic acid (DTPA), glycine, L-histidine, picolinic acid (2-pyridinecarboxylic acid) and N-(benzylimino)diacetic acid. In order to reach additional information on the complexation processes, the chemometrical method MCR-ALS (multivariate curve resolution with alternating least squares) was used for data processing and interpretation, which permitted to obtain both the dynamic picture of complexation and stoichiometries of formed species. [Copyright &y& Elsevier]

Abstract: Interactions between small molecules with biopolymers e.g. the bovine serum albumin (BSA protein), are important, and significant information is recorded in the UV–vis and fluorescence spectra of their reaction mixtures. The extraction of this information is difficult conventionally and principally because there is significant overlapping of the spectra of the three analytes in the mixture. The interaction of berberine chloride (BC) and the BSA protein provides an interesting example of such complex systems. UV–vis and fluorescence spectra of BC and BSA mixtures were investigated in pH 7.4 Tris–HCl buffer at 37°C. Two sample series were measured by each technique: (1) [BSA] was kept constant and the [BC] was varied and (2) [BC] was kept constant and the [BSA] was varied. This produced four spectral data matrices, which were combined into one expanded spectral matrix. This was processed by the multivariate curve resolution–alternating least squares method (MCR–ALS). The results produced: (1) the extracted pure BC, BSA and the BC–BSA complex spectra from the measured heavily overlapping composite responses, (2) the concentration profiles of BC, BSA and the BC–BSA complex, which are difficult to obtain by conventional means, and (3) estimates of the number of binding sites of BC. [Copyright &y& Elsevier]

Abstract: A promising application of the multivariate curve resolution based on alternating least squares (MCR-ALS) method is reported for the analysis of the temperature-dependent conformational changes in poly(l-lysine) (PLL). The MCR-ALS approach has enabled detection of three structural components developed during the melting experiment. Most important is an infrared signature of the intermediate component described as a mixture of native α-helical conformation and its extended forms. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an enhanced line search algorithm to accelerate the convergence of the alternating least squares (ALS) algorithm, which is often used to decompose a tensor in a sum of contributions. This scheme can be used for the computation in the complex case of the Parallel Factor model or the more general block component model. We then illustrate the performance of the algorithm in the context of blind separation-equalization of convolutive DS-CDMA mixtures. [Copyright &y& Elsevier]

Abstract: This paper reports the validation of the results obtained by combining near infrared spectroscopy and multivariate curve resolution-alternating least squares (MCR-ALS) and using high performance liquid chromatography as a reference method, for the model reaction of phenylglycidylether (PGE) and aniline. The results are obtained as concentration profiles over the reaction time. The trueness of the proposed method has been evaluated in terms of lack of bias. The joint test for the intercept and the slope showed that there were no significant differences between the profiles calculated spectroscopically and the ones obtained experimentally by means of the chromatographic reference method at an overall level of confidence of 5%. The uncertainty of the results was estimated by using information derived from the process of assessment of trueness. Such operational aspects as the cost and availability of instrumentation and the length and cost of the analysis were evaluated. The method proposed is a good way of monitoring the reactions of epoxy resins, and it adequately shows how the species concentration varies over time. [Copyright &y& Elsevier]

Abstract: Soft- and hard-modelling strategy was applied to near-infrared spectroscopy data obtained from monitoring the reaction between glycidyloxydimethylphenyl silane, a silicon-based epoxy monomer, and aniline. On the basis of the pure soft-modelling approach and previous chemical knowledge, a kinetic model for the reaction was proposed. Then, multivariate curve resolution-alternating least squares optimization was carried out under a hard constraint, that compels the concentration profiles to fulfil the proposed kinetic model at each iteration of the optimization process. In this way, the concentration profiles of each species and the corresponding kinetic rate constants of the reaction, unpublished until now, were obtained. The results obtained were contrasted with 13C NMR. The joint interval test of slope and intercept for detecting bias was not significant (α =5%). [Copyright &y& Elsevier]

Abstract: In some antenna array-based wireless communication systems the received signal is multidimensional and can be treated as a tensor (3D array) instead of a matrix (2D array). In this paper, we make use of a generalized tensor decomposition known as constrained Block-PARAFAC and propose a tensor (3D) model for the signal received by three types of wireless communication systems. The considered wireless communication systems are multiuser systems subject to frequency-selective multipath and employing multiple receiver antennas together with (i) oversampling or (ii) direct-sequence spreading or (iii) multicarrier modulation. The proposed modeling approach aims at unifying the received signal model of these systems into a single PARAFAC model. We show that the proposed model has a constrained structure, where model constraints and associated dimensions depend on each particular system. The proposed constrained Block-PARAFAC model is demonstrated by expanding the tensor using Kronecker products of canonical vectors. As an application of this model to tensor signal processing, a new tensor-based receiver is proposed for blind multiuser equalization, which combines PARAFAC-based modeling with a subspace method. Simulation results are presented to illustrate the performance of the proposed blind receiver. [Copyright &y& Elsevier]

Abstract: The analysis of data from analytical equipment will be an important factor in the execution of metabolomics. Self-modeling curve resolution (SMCR) is one of the theoretical techniques of chemometrics and has recently been applied to the data of hyphenated chromatography techniques. Alternating least squares (ALS) is a classical SMCR method. In ALS, however, different solutions are produced depending on randomly chosen initial values. Simulation in the present study showed that the use of a normalized constraint in calculating ALS was effective in avoiding this problem. We also improved the ALS algorithm by adding a regularized term (regularized ALS: RALS). Independent component analysis (ICA) is a comparatively new method and has been discussed very actively by information science researchers, but has still been applied only in very few cases to curve resolution problems in chemometrics studies. We applied RALS with a normalized constraint and ICA to the HPLC-DAD data of Haematococcus pluvialis metabolites and obtained a high accuracy of peak detection, suggesting that these curve resolution methods are useful for identification of metabolites in metabolomics. [Copyright &y& Elsevier]

Abstract: Multivariate curve resolution-alternating least squares (MCR-ALS) is applied to solve coelution problems in liquid chromatograpy with diode array detection (DAD) and mass spectrometry (MS). Fusion of DAD and MS detector signals improved results versus those obtained using only one of the two detector signals. Application of wavelet transform to MS data before its fusion with DAD data, further help to facilitate the resolution and quantitation of the coeluted compounds under study, besides a decrease of time of analysis. Mixtures of biocide compounds in standard mixtures and in environmental samples (sediment and wastewater samples) were analyzed with estimated quantitation errors below 12%. [Copyright &y& Elsevier]

Abstract: This article discusses the potential of using sequential injection analysis (SIA) for generating second-order data. To treat these data, we used multivariate curve resolution with alternating least squares (MCR–ALS) as the chemometric tool. This combination can be used for both qualitative and quantitative analyses, since it provides concentration and spectra profiles for the various species. By combining these techniques (SIA–MCR–ALS), several analytes can be determined simultaneously in the presence of interferents without the need to pretreat the sample. We describe the state of the art of both techniques by reviewing the literature since 2004 and the necessary conditions for applying chemometric tools to treat this type of data. We also discuss the advantages and disadvantages of this combined technique and examine the future prospects of SIA and MCR–ALS. [Copyright &y& Elsevier]

Abstract: Multivariate curve resolution-alternating least squares (MCR-ALS) is shown to be a powerful tool to resolve coelution problems in liquid chromatograpy–mass spectrometry (LC–MS) in scan mode. This investigation was performed using two types of LC columns, one traditional LC column of 25cm length with a slow gradient and a shorter LC column of 7.5cm with a rapid gradient which allowed much faster analysis and save of reagents and solvents. Mixtures of multiple biocide compounds were simultaneously analyzed in standard mixtures and in environmental samples (sediment and wastewater samples) with little sample pretreatment. Using the more traditional LC 25cm column, all biocide compounds were properly resolved by MCR-ALS and quantitatively analyzed with estimated errors always below 20%. When fast chromatography (LC column of 7.5cm) was used, MCR-ALS resolution of the more strongly coeluted compounds was also achieved but limitations were found in their simultaneous quantitative determination, specially for environmental samples. [Copyright &y& Elsevier]

Abstract: This study describes a method for calculating the band boundaries of feasible solutions for spectra and concentration profiles obtained by Multivariate Curve Resolution–Alternating Least Squares (MCR–ALS) analysis of a spectroscopic NIR data set. The data set is obtained by monitoring in situ the model reaction between phenyl glycidyl ether (PGE) and aniline. As this system happened to be rank-deficient, the resolution strategy used matrix augmentation. The calculation of band boundaries of feasible solutions is extended here to the simultaneous analysis of multiple data matrices. The boundaries were obtained by a non-linear constrained non-linear optimisation. The influence that the number and type of data matrices in the simultaneous analysis have on the amplitude of band boundaries is also discussed. [Copyright &y& Elsevier]

Abstract: Mixtures of the surfactant classes coconut diethanolamide, cocamido propyl betaine and alkylbenzene sulfonate were separated by capillary electrophoresis in several media containing organic solvents and anionic solvophobic agents. Good resolution between both the surfactant classes and the homologues within the classes was achieved in a BGE containing 80mM borate buffer of pH 8.5, 20% n-propanol and 40mM sodium deoxycholate. Full resolution, assistance in peak assignment to the classes (including the recognition of solutes not belonging to the classes), and improvement of the signal-to-noise ratio was achieved by multivariate data analysis of the time–wavelength electropherograms. Cubic smoothing splines were used to develop an algorithm capable of automatically modelling the two-way background, which increased the sensitivity and reliability of the multivariate analysis of the corrected signal. The exclusion of significant signals from the background model was guaranteed by the conservativeness of the criteria used and the safeguards adopted all along the point selection process, where the CSS algorithm supported the addition of new points to the initially reduced background sample. Efficient background modelling made the application of multivariate deconvolution within extensive time windows possible. This increased the probability of finding quality spectra for each solute class by orthogonal projection approach. The concentration profiles of the classes were improved by subsequent application of alternating least squares. The two-way electropherograms were automatically processed, with minimal supervision by the user, in less than 2min. The procedure was successfully applied to the identification and quantification of the surfactants in household cleaners. [Copyright &y& Elsevier]

Non-absorbing alkyl ether sulfates (AES) can be separated using anthraquinone-2-carboxylic acid (AQCA) as a probe; however, absorbing alkyl benzene sulfonates (ABS), if present, interfere indirect detection of most AES oligomers. Overcoming of this interference, as well as the simultaneous characterisation and evaluation of AES, fatty acids and ABS, was accomplished by using a diode-array detector and the procedures here discussed. First, it was shown that ABS can be made undetectable by using a 9 nm wide and 227 nm centred charge-absorptivity null-balance detection window (NBDW), where its contribution to the absorbance cancels the dilution effects that its presence induces on the signal of the background chromophore (BGC). Two other procedures, not requiring any prior knowledge on the nature of the absorbing interference, were also addressed. In the first one, the NBDW procedure was emulated by software, by treating the time–wavelength data matrix stored during the experimental run, and in the second one, both the ABS and BGC spectra, and the concentration profiles of ABS and the non-absorbing solutes, were recovered by orthogonal projection approach (OPA) and alternating least squares (ALS). The OPA–ALS processing provided the deconvolved signals and the wavelengths required to implement the experimental and software-emulated NBDW procedures. A composite ABS spectrum and a mixed concentration profile of the non-absorbing solutes, that involves mutual ABS–BGC dilution effects are enclosed in the OPA–ALS straightforward solutions. The pure spectra and concentration profiles were finally retrieved by crossed orthogonalisation. For the NBDW procedures, the limits of detection (S/N=3) for AES oligomers overlapped by 1500 μg ml−1 ABS were of ca. 10 μM AES. Using decyl sulfate as internal standard, the relative standard deviation for AES in an ABS containing industrial sample was 4.5%. The procedures here described are useful to remove the interference produced by any absorbing solute when overlapped with indirectly detected solutes in both capillary electrophoresis (CE) and HPLC. [Copyright &y& Elsevier]

Diffusion-ordered spectroscopy (DOSY) NMR is based on a pulse-field gradient spin-echo NMR experiment, in which components experience diffusion. Consequently, the signal of each component decays with different diffusion rates as the gradient strength increases, constructing a bilinear NMR data set of a mixture. By calculating the diffusion coefficient for each component, it is possible to obtain a two-dimensional NMR spectrum: one dimension is for the conventional chemical shift and the other for the diffusion coefficient. The most interesting point is that this two-dimensional NMR allows non-invasive “chromatography” to obtain the pure spectrum for each component, providing a possible alternative for LC-NMR that is more expensive and time-consuming. Potential applications of DOSY NMR include identification of the components and impurities in complex mixtures, such as body fluids, or reaction mixtures, and technical or commercial products, e.g. comprising polymers or surfactants.Data processing is the most important step to interpret DOSY NMR. Single channel methods and multivariate methods have been proposed for the data processing but all of them have difficulties when applied to real-world cases. The big challenge appears when dealing with more complex samples, e.g. components with small differences in diffusion coefficients, or severely overlapping in the chemical shift dimension. Two single channel methods, including SPLMOD and continuous diffusion coefficient (CONTIN), and two multivariate methods, called direct exponential curve resolution algorithm (DECRA) and multivariate curve resolution (MCR), are critically evaluated by simulated and real DOSY data sets. The assessments in this paper indicate the possible improvement of the DOSY data processing by applying iterative principal component analysis (IPCA) followed by MCR-alternating least square (MCR-ALS). [Copyright &y& Elsevier]

This paper describes an improved three-way alternating least-squares multivariate curve resolution algorithm that makes use of the recently introduced multi-dimensional arrays of MATLAB®. Multi-dimensional arrays allow for a convenient way to apply chemically sound constraints, such as closure, in the third dimension. The program is designed for kinetic studies on liquid chromatography with diode array detection but can be used for other three-way data analysis. The program is tested with a large number of synthetic data sets and its flexibility is demonstrated, especially when non-trilinear data sets are fit. In this case, the algorithm finds a solution with a better fit than direct trilinear decomposition (DTD). When trilinear data are used, the optimal fit is not as good as when a direct decomposition method is used. Most real data sets, however, have some degree of non-trilinearity. This makes this method a better choice to analyze non-trilinear, three-way data than direct trilinear decomposition. [Copyright &y& Elsevier]

PARAFAC2 is a well-established method for specific type of tensor decomposition problems, for example when observations have different lengths or measured profiles slightly change position in the multi-way data. Most commonly used PARAFAC2-ALS algorithms are very slow. In this paper, we propose novel implementations of extrapolation-based PARAFAC2 algorithms. Next to the frequently implemented PARAFAC2-ALS, also Hierarchical ALS is investigated for PARAFAC2. We show that the newly proposed implementation of All-at-once Nesterov-like extrapolation PARAFAC2-ALS algorithm achieves the fastest convergence speed whilst maintaining a low fraction of local minima solutions. This new method is shown to be 13 times faster on average compared to a PARAFAC2-ALS algorithm without acceleration, whereas the commonly used N-way toolbox line search extrapolation PARAFAC2-ALS algorithm obtains only a 3 times speedup on the same simulated dataset. Furthermore, the proposed method is shown to outperform the latest extrapolation acceleration PARAFAC2 algorithms available in literature. A comprehensive investigation and comparison is performed of all the proposed extrapolation algorithms, using both simulated and real (GC-MS) data. To the best of our knowledge, this is the first paper that systematically investigates extrapolation acceleration PARAFAC2-ALS and PARAFAC2-HALS algorithms. • Novel implementations of extrapolation-based PARAFAC2 algorithms are established using different optimization techniques. • A comprehensive investigation and comparison is made of all the proposed extrapolation-based PARAFAC2-ALS and PARAFAC2-HALS algorithms. • The performance of the algorithms is tested using real and simulated GC-MS datasets in terms of algorithm speed, number of local minima, convergence ability and fitting process. • Proposed All-at-once Nesterov-like extrapolated PARAFAC2-ALS algorithm converges the fastest whilst maintaining a low fraction of local minima solutions, outperforming the latest extrapolated PARAFAC2 algorithms significantly. [ABSTRACT FROM AUTHOR]

The effect of physicochemical factors and use of skim milk powder on milk rennet-coagulation was investigated combining near infrared (NIR) spectroscopic monitoring and Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS). Coagulum formation has been studied by reference approaches (Formagraph and fundamental rheology) and with NIR spectroscopy on unaltered reconstituted milk samples, pasteurized samples, samples with calcium chloride addition and samples of reconstituted milk mixed with fresh milk. The MCR-ALS models successfully described the process evolution, explaining more than 99.9% of variance. The MCR-ALS profiles revealed to be significantly directly correlated with Formagraph and rheological data (p < 0.001) and allowed assessing the significant effect (p < 0.05) of the milk powder type on the coagulation occurrence and the non-significance (p > 0.05) of the CaCl 2 concentration level added and the heat treatment applied. The MCR-ALS models calculated for the coagulation trials of pasteurized skimmed milk mixed with reconstituted milk samples highlighted shorter coagulation times with the increasing of reconstituted milk amount (from 4.3-6.6 min to 2–5 min). Profiles extracted from MCR-ALS models developed for a wide range of coagulation conditions proved to be suitable non-destructive, non-invasive and on-line tools to evaluate the rennet-induced coagulation of reconstituted milks. • Assessment of milk powder type, CaCl2 and heat treatment effects on coagulation. • Different ratios of milk and reconstituted milk powder affect coagulation. • FT-NIR spectroscopy coupled with MCR-ALS successfully monitors milk coagulation. • Good correlation between FT-NIR spectroscopy, rheology and Formagraph. • The proposed method is suitable for an on-line application to control coagulation. [ABSTRACT FROM AUTHOR]

Interval estimation in Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) is a challenging problem. Several algorithms including Bayesian, Monte-Carlo, bootstrap and jackknife resampling approaches have been proposed previously to address this problem in MCR. In the present contribution, constructing the confidence intervals (CIs) in MCR-ALS resolved profiles using the principles of error propagation in linear least squares (LS) parameter estimation is proposed. In MCR-ALS, every set of profiles in the row subspace (scores) can be considered as coefficients for estimating their counterparts in the columns subspace (loadings) and vice versa. Therefore, it should be possible to calculate the CIs for these coefficients (scores or loadings) using the principles of error propagation in LS. The confidence intervals of the coefficients in linear regression are directly related to the inverse of the matrix of sums of squares and sums of cross products of independent variables and to the standard deviation of the residuals. This idea has been successfully applied in this work for the construction of the CIs of the resolved profiles in the MCR-ALS algorithm. The proposed approach is named 'Confidence Intervals based on Least Squares' (CILS). The weighted version of this approach has also been implemented and named as CIWLS. The latter method can be used for handling datasets with a known type of error structure. The performances of the CILS and CIWLS approaches are evaluated in this work for the calculation of the CIs for several simulated three component LC-MS and LC-DAD datasets, with different homo- and heteroscedastic noise levels. The CIs obtained by CILS and CIWLS are compared with those obtained by the Monte-Carlo noise addition method. The empirical coverage probabilities of the CIs are also computed to check if the calculated CIs achieve the nominal confidence level. The average standard errors (ASE) are used as measures of the level of uncertainty (precision) in the recovered profiles. The results obtained in this work revealed that the CIs obtained by the CILS method are in agreement with those obtained by the Monte-Carlo approach. The main advantage of the CILS method is that the calculations are faster and require less computation time. Finally, the performance of the CIWLS algorithm was assessed in the analysis of a real environmental dataset for the source apportionment of particulate matter (PM) in air samples collected in Northern Spain. The results obtained by the CIWLS method were in agreement with those previously reported for this real dataset and the CIs of the contribution and composition profiles of the PM10 sources were properly estimated. • A new method was developed for calculation of the confidence intervals in MCR-ALS solutions using the principles of error propagation in linear least squares (CILS). • The weighted version of the method, CIWLS was developed for calculation of CIs when the error structure is known. • The performances of CILS and CIWLS were evaluated using simulated and real datasets. • Average coverage probabilities were calculated for addressing the accuracy of CILS and CIWLS methods. • The calculated CIs were compared with those obtained using Monte-Carlo noise addition technique. [ABSTRACT FROM AUTHOR]

Traffic flow data, as an important data source for the research and development of intelligent transportation systems, contain abundant multi-mode features. In this paper, a high-dimensional multi-mode tensor is used to represent traffic flow data. The Tucker tensor decomposition least squares algorithm is used to establish the tensor alternating least squares GM (1,1) model by combining the modelling mechanism of the grey classical model GM (1,1) with the algorithm, and the modelling steps are obtained. To demonstrate the effectiveness of the new model, first, the multi-mode traffic flow data are represented by the tensor model, and the correlation of the traffic flow data is analysed. Second, two short-term traffic flow prediction cases are analysed, and the results show that the performance of the GM (1, 1) model based on the tensor alternating least squares algorithm is obviously better than that of the other models. Finally, the original tensor data and the approximate tensor data during the peak period from 8:00 to 8:30 a.m. for six consecutive Mondays are selected as the experimental data, and the effect of the new model is much better than that of the GM (1,1) model of the original tensor data. • The tensor alternating quadratic GM(1,1) model was proposed. • High-dimensional tensor multi-mode is used to represent traffic flow data. • The organic combination of tensor alternating quadratic method and grey model. • The new model can effectively predict the short-term traffic flow. [ABSTRACT FROM AUTHOR]

Last decade has witnessed a drastically increasing development of smart devices, while related mobile applications have emerged significantly in people's daily life. As such, understanding the pattern of mobile application usage and related online behavior is of great importance for a variety of purposes, such as application engineering, resource optimization, and marketing. Existing research of online usage discovery includes surveys from end-users, application provider-related analysis, and usage log mining. These works, however, suffer from some limitations, such as lacking of user socio-economics background, insufficient coverage and sample bias, etc. A novel and comprehensive application-usage profiling algorithm, termed as TAG, is proposed in this study to investigate online behavior. The proposed algorithm consists of three major steps: (i) T-step: representing usage data as a Term Frequency-Inverse Document Frequency based matrix; (ii) A-step: applying Alternating Least Squares factorization technique to reduce data sparseness and dimension; and last (iii) G-step: utilizing a smoothed Gaussian Mixture Model for clustering purpose. The performance of the proposed TAG algorithm is evaluated, taking a national dataset generated from 31,280 devices and 30,155 applications over 30 months as an example. Experimental results demonstrate that the proposed algorithm outperforms existing methods via forming accurate usage groups from school-level online behavior. As such, the superior clustering outcome demonstrates the flexibility and applicability of the proposed work for understanding online pattern using complex application usage data. Resultant knowledge can in turn be used to inform decision making and improve application development. [ABSTRACT FROM AUTHOR]