A novel approach to the quantification of industrial mixtures from the Vinyl Acetate Monomer (VAM) process using Near Infrared spectroscopic data and a Quantitative Self Modeling Curve Resolution (SMCR) methodology

A convergence criterion in alternating least squares (ALS) by global phase angle

Self-modeling curve resolution (SMCR) by particle swarm optimization (PSO)

Non-negative matrix factorization (NMF) is a problem to obtain a representation of data using non-negativity constraints. Since the NMF was first proposed by Lee, NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. Recent years, many variants of NMF have been proposed. Common methods are: iterative multiplicative update algorithms, gradient descent methods, alternating least squares (ANLS). Since alternating least squares has nice optimization properties, various optimization methods can be used to solve ANLS's subproblems. In this paper, we propose a modified subspace Barzilai-Borwein for subproblems of ANLS. Moreover, we propose a modified strategy for ANLS. Global convergence results of our algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

Optimization of a reaction solvent is typically performed when a chemistry if progressed from discovery to scale up. Typically, a large number of solvents are screened to determine which solvent gives the highest rate and yield. Samples are drawn out during the reaction and are analyzed by HPLC. This screening method suffers from a long idle time as the HPLC methods are long and is limited to a small number of samples due to the large number of HPLC samples generated. What is described in this work is an in-situ UV/vis method to perform an on-line analysis of multiple reactions to quickly determine which solvents give the fastest rate. A fiber optic probe is placed directly into the reaction vessel and UV/vis spectra are collected simultaneously from each reaction. Composition profiles and pure component spectra of reactants, intermediates, and products are estimated, using iterative target transformation factor analysis (ITTFA), a type of self- modeling curve resolution (SMCR), without the aid of referee measurements or standards. The results indicate that the method can successfully predict which solvent and can be used as a broad screening tool for the optimization of the reaction. Pairwise analysis of consecutive batches can be used to perform standardless comparisons between the two batches to determine if the reaction proceeded faster or slower, and made more or less product.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Different approaches have been proposed during recent years to improve the solutions obtained by multivariate curve resolution methods, among them studies on circumstances that result in unique answers are of particular importance. Three so‐called resolution theorems proposed by Rolf Manne comprehensively discuss and survey these conditions. Despite the importance of these theorems, they have not attracted much attention in the literature. In this work, we have returned to the resolution theorems by using visualization tools for calculation and demonstration the area of feasible solutions in a simulated three component system. The effect of selectivity and local rank constraints on rotational ambiguity in the results of self modeling curve resolution methods is the focus. Copyright © 2013 John Wiley & Sons, Ltd.

The main task of environmental and geoscience applications is efficient and accurate quantitative classification of earth surfaces and spatial phenomena. In the past decade, there has been a significant interest in employing hyperspectral unmixing (HU) to retrieve accurate quantitative information latent in hyperspectral imagery data. Recently, the ground-truth and laboratory measured spectral signatures promoted by advanced algorithms are proposed as a new path toward solving the unmixing problem of hyperspectral imagery in semisupervised fashion. This paper suggests that the sensitivity of sparse unmixing techniques provides an ideal approach to extract and identify dust settled over/upon green vegetation canopy using hyperspectral airborne data. Among the available techniques, this study presents the results of seven selected algorithms: 1) non-negative matrix factorization (NMF); 2) L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sparsity-constrained NMF (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1_</sub> NMF); 3) L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> sparsity-constrained NMF (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> _NMF); 4) graph regularized NMF (G_NMF); 5) structured sparse NMF (SS_NMF); 6) alternating least-square (ALS); and 7) Lin's projected gradient (LPG). The performance is evaluated on real hyperspectral imagery data via detailed experimental assessment. The results compared with performances of selected conventional unmixing techniques.

Resolution of multicomponent peaks by orthogonal projection approach, positive matrix factorization and alternating least squares

In the paper we present new Alternating Least Squares (ALS) algorithms for Nonnegative Matrix Factorization (NMF) and their extensions to 3D Nonnegative Tensor Factorization (NTF) that are robust in the presence of noise and have many potential applications, including multi-way Blind Source Separation (BSS), multi-sensory or multi-dimensional data analysis, and nonnegative neural sparse coding. We propose to use local cost functions whose simultaneous or sequential (one by one) minimization leads to a very simple ALS algorithm which works under some sparsity constraints both for an under-determined (a system which has less sensors than sources) and overdetermined model. The extensive experimental results confirm the validity and high performance of the developed algorithms, especially with usage of the multi-layer hierarchical NMF. Extension of the proposed algorithm to multidimensional Sparse Component Analysis and Smooth Component Analysis is also proposed.

Nonnegative matrix factorization (NMF) is an unsupervised learning method for decomposing high-dimensional nonnegative data matrices and extracting basic and intrinsic features. Since image data are described and stored as nonnegative matrices, the mining and analysis process usually involves the use of various NMF strategies. NMF methods have well-known applications in face recognition, image reconstruction, handwritten digit recognition, image denoising and feature extraction. Recently, several projective NMF (P-NMF) methods based on positively constrained projections have been proposed and were found to perform better than the standard NMF approach in some aspects. However, some drawbacks still affect the existing NMF and P-NMF algorithms; these include dense factors, slow convergence, learning poor local features, and low reconstruction accuracy. The aim of this paper is to design algorithms that address the aforementioned issues. In particular, we propose two embedded P-NMF algorithms: the first method combines the alternating least squares (ALS) algorithm with the P-NMF update rules of the Frobenius norm and the second one embeds ALS with the P-NMF update rule of the Kullback–Leibler divergence. To assess the performances of the proposed methods, we conducted various experiments on four well-known data sets of faces. The experimental results reveal that the proposed algorithms outperform other related methods by providing very sparse factors and extracting better localized features. In addition, the empirical studies show that the new methods provide highly orthogonal factors that possess small entropy values.

Spectrophotometric determination of a mixture of weak acids using multivariate calibration and flow injection analysis titration

Application of regularized alternating least squares and independent component analysis to HPLC-DAD data of Haematococcus pluvialis metabolites

A multichannel blind source separation algorithm based on the multichannel non‐negative matrix factorisation (NMF) model and an alternating least squares (ALS) method is developed. To develop the proposed algorithm, the multichannel NMF (MC‐NMF) model is modified with stacked matrix notation. In the model, all parameters – frequency basis, time basis and mixing matrix – are estimated using the ALS method. The proposed MC‐NMF algorithm is evaluated using an ‘underdetermined speech and music mixture’ dataset from the International Signal Separation Evaluation Campaign 2013 (SiSEC 2013). Experimental results show that the proposed algorithm outperforms the conventional NMF algorithms.

The products formed from the reactions of OH radicals with vinyl acetate and allyl acetate have been studied in a 1080 L quartz-glass chamber in the presence and absence of NO(x) using in situ FTIR spectroscopy to monitor the reactant decay and product formation. The yields of the primary products formed in the reaction of OH with vinyl acetate were: formic acetic anhydride (84 ± 11)%; acetic acid (18 ± 3)% and formaldehyde (99 ± 15)% in the presence of NO(x) and formic acetic anhydride (28 ± 5)%; acetic acid (87 ± 12)% and formaldehyde (52 ± 8)% in the absence of NO(x). For the reaction of OH with allyl acetate the yields of the identified products were: acetoxyacetaldehyde (96 ± 15)% and formaldehyde (90 ± 12)% in the presence of NO(x) and acetoxyacetaldehyde (26 ± 4)% and formaldehyde (12 ± 3)% in the absence of NO(x). The present results indicate that in the absence of NO(x) the main fate of the 1,2-hydroxyalkoxy radicals formed after addition of OH to the double bond in the compounds is, in the case of vinyl acetate, an α-ester rearrangement to produce acetic acid and CH(2)(OH)CO(•) radicals and in the case of allyl acetate reaction of the radical with O(2) to form acetic acid 3-hydroxy-2-oxo-propyl ester (CH(3)C(O)OCH(2)C(O)CH(2)OH). In contrast, in the presence of NO(x) the main reaction pathway for the 1,2-hydroxyalkoxy radicals is decomposition. The results are compared with the available literature data and implications for the atmospheric chemistry of vinyl and allyl acetate are assessed.

Rapid and accurate estimation of plant potassium accumulation (PKA) using hyperspectral remote sensing is of significance for the precise management of crop K fertilizer. This study focused on the separation of non-negative matrix factorization (NMF) for hyperspectral reflectance from the ground and unmanned aerial vehicle (UAV) platforms and its mitigation effect on the water and soil background. Pure vegetation spectra were extracted from the canopy mixed spectra using NMF, and then a partial least-squares regression (PLSR) model was established based on the extracted vegetation spectra and rice PKA to construct an estimation model of rice PKA. The results showed that the green light and red edge bands contributed significantly to the rice PKA estimation. NMF could effectively extract pure vegetation and water and soil spectra from mixed spectra, and enhance the green peak, red valley, and red edge information of the extracted vegetation spectra. Compared with spectral indices, the PLSR performed best for ground and UAV data. Besides, the R2 of the PLSR model based on NMF-extracted vegetation spectra increased by 15.15% to 0.76%, and the verified RMSE and RE decreased by 16.93% and 16.77% to 3.19 g m−2 and 45.07%, respectively. Hyperspectral dataset testing from different years, growth stages and varieties, and UAV platforms showed that NMF could improve the estimation accuracy of rice PKA. This study showed that NMF could be applied to both ground and UAV hyperspectral platforms to improve the estimation accuracy of rice K nutrition.

Various independent component analysis (ICA) algorithms (MILCA, JADE, SIMPLISMA, RADICAL) are applied for simultaneous spectroscopic determination of two groups of transition metals: Co(II)–Fe(III)–Cu(II)–Zn(II)–Ni(II) and Pt(IV)–Pd(II)–Ir(IV)–Rh(III)–Ru(III)) in complex mixtures. The analysis is based on the decomposition of spectra of multicomponent mixtures in the UV-VIS region based on the natural absorbance of metal salts, or, when a better sensitivity is desirable, based on the absorbance of their complexes with 4-(2-pyridylazo)resorcinol (PAR) and ethylenediaminetetraacetic acid (EDTA). Good quality spectral resolution of up to seven-component mixtures was achieved (correlation coefficients between resolved and experimental spectra are not less than 0.90). In general, the relative errors in the recovered concentrations are at levels of only several percent. While being superior to other ICA algorithms, MILCA is comparable or even outperforms other classical chemometric methods for quantitative analysis that were used for comparison purposes (Partial Least Squares (PLS), Principal Component Regression (PCR), Alternating Least Squares (ALS)). Simultaneous quantitative analysis is possible for mixtures containing up to five metals in the broad concentration ranges even when individual spectra show 99% overlap. A small excess of derivatization reagent (till threefold excess to the sum of metal concentrations) is optimal to obtain good quantitative results. The proposed method was used for analysis of authentic samples (multimineral supplements and platinum concentrates). The resolved ICA concentrations match well with the labelled amounts and the results of other chemometric methods (ALS, PLS). ICA decomposition considerably improves the application range of spectroscopy for metal quantification in mixtures.