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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). Image 1 • Joint selection of essential samples and essential variables in hyperspectral images. • Convex hull provides reduced rate of over 99%. • MCR-ALS can be easily applied on the reduced data sets. • The full-size distribution maps and spectral profiles can be readily obtained. [ABSTRACT FROM AUTHOR]

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. Image 1 • Initialization is an important phase in multivariate curve resolution. • Accurate results are possible even with substantial rotational ambiguity. • Initialization with pure variables implicitly benefits from selectivity. • Pure variables are helpful depending on the data mode for their estimation. [ABSTRACT FROM AUTHOR]

Self‐modeling curve resolution (SMCR) techniques are widely applied for resolving chemical data to the pure‐component spectra and composition profiles. In most circumstances, there is a range of mathematical solutions to the curve resolution problem. The mathematical solutions generated by SMCR obey the applied constraints coming from a priori physicochemical information about the system under investigation. However, several studies demonstrate that a unique solution can be obtained by implementing some constraints such as trilinearity, equality, zero concentration region, correspondence, local‐rank, and non‐negativity under data‐based uniqueness (DBU) condition. In this research, a general rule for uniqueness (GRU) is proposed to unify all the different information that lead to a unique solution in one framework. Moreover, GRU can be a guide for developing new constraints in SMCR to get more accurate solutions. The authors are delighted to dedicate this manuscript to Professor Paul J. Gemperline in recognition of his significant contributions to the field of chemometrics. We believe that the chemometrics society's success in addressing its mission owes a great deal to his vision, passion for learning and teaching, and extensive scientific efforts over the years. We honor his friendship and generous supports. [ABSTRACT FROM AUTHOR]

Modern analytical instruments provide measurement data arrays with full of hidden and redundant information. Multivariate curve resolution (MCR) techniques decompose data set to physic‐chemically meaningful abstract profiles. On the other hand, for such data matrices, Borgen‐Rajkó self‐modeling curve resolution (SMCR) techniques reveal all possible solutions analytically under the minimal assumption. Although Lawton‐Sylvestre (LS) and Borgen methods have been proposed for the non‐negative curve resolution of two‐component and three‐component systems, there is still a great deal of interest to include further restrictions on the Borgen‐Rajkó SMCR. As modern hyphenated analytical instruments produce multiway (eg, three‐way) arrays, multiway analysis (eg, trilinear decomposition) was received much more popularity by chemists. This contribution is decicated to the extension of the Borgen algorithm to the trilinear data sets. The Borgen method incorporating trilinearity constraint is approached in an analogy to the trilinear Lawton‐Sylvester method. The proposed analytical triadic decomposition is applied to the simulated three‐way arrays with full rank and rank overlap (a type of rank deficiency) loadings. Finally, the proposed algorithm is further exemplified with a three‐component spectrofluorimetric study of acid‐base equilibrium of the pyridoxine. Investigating feasible regions of the simulated and experimental three‐component arrays reveal interesting additional information. Borgen method incorporating trilinearity constraint is approached in an analogy to the trilinear Lawton‐Sylvester method. The proposed analytical triadic decomposition is applied to the simulated three‐way arrays with full rank and rank overlap (a type of rank‐deficiency) loadings. Finally, the proposed algorithm is further exemplified with a three‐component spectrofluorimetric study of acid‐base equilibrium of the pyridoxine. Investigating feasible regions of the simulated and experimental three‐component arrays reveal interesting additional information. [ABSTRACT FROM AUTHOR]

The 8–17E DNAzyme is a temperature-dependent DNA metalloenzyme catalyzing RNA trans esterification in the presence of Pb2+ metal ions. Labeling the stems of the substrate and DNAzyme with the Cy3 and Cy5 respectively, the considered DNAzyme was studied by the fluorescence spectroscopy. The temperature-dependent variability of the Pb2+-specific 8–17E DNAzyme catalytic sensor was investigated trough a number of successive temperature fluctuations from 4 to 25 °C to obtain information. Investigating underlined biochemical system reveals that in this sensor, free single strands Enzyme (Cy5-E) and Substrate (Cy3-S) have higher fluorescence intensities than hybridized forms, suggesting that the fluorophores are in a contact quenched. Increasing the temperature has three effects: 1) Fluorescence intensities for the free fluorophores were reduced, 2) stability of the hybridized form was reduced and cleavage of substrate in presence of Pb2+was occurred, and 3) conformation of ES hybridized form was changed (before cleavage). As a result of conformation changes in ES, S was more affected than E in the ES. Pb2+ ion shows quenching effect on both fluorophores and in the absence of N2(g) purge the effect was more considerable. A main goal that we had in mind was to find if significantly lower concentrations of Pb2+ and ES, compared to previous reports, can generate any observable cleavage in substrate. Analysis of the cleavage reaction for 50 nM ES indicates that S is cleaved at 25 °C in presence of N2(g) and 0.5 μM Pb2+, while in same condition no apparent change occurs in the 4 or 10 °C. The rapid, sensitive and low cost strategy presented here can be applicable to study temperature-dependent behavior of other nucleic acid-based biosensors. [ABSTRACT FROM AUTHOR]

G-quadruplexes are formed by association of DNA strands containing multiple contiguous guanines. The capability of drugs to induce formation or stabilize G-quadruplexes is an active area of cancer therapy investigation. We evaluated interaction between two cationic tetrapyridinoporphyrazines with Na and K forms of human telomeric G-quadruplex DNA by chemometrics method. An antiparallel quadruplex structure was found to be stabilized more greatly by these two isomers in the presence of K and Na ions. Equilibrium model of a ligand binding with DNA oligomer has been considered as a process of small molecule adsorption on to a lattice of multiple binding sites. In multivariate analysis methods, it is accounted this assertion that during saturation of the macromolecule by a ligand should expect effect of cooperativity due to changes in DNA conformation or the mutual influence between bound ligands. Such phenomenon cannot be entirely described by the classical stepwise complex formation model. From the results of absorption and circular dichroism measurements, the unique site for the ligand binding is suggested to be the intercalating in guanine tetrad plane quadruplex. We found a 2:1 binding stoichiometry for both ligands and Tel22. [ABSTRACT FROM AUTHOR]

Several curve resolution techniques have been developed to analyze higher-order data structures, among which one can name parallel profiles with linear dependencies (PARALIND). The PARALIND is a variant of the Parallel Factor Analysis (PARAFAC) to cope with linear dependencies. Applying a PARAFAC model with different random initializations to a noisy three-way data with linearly dependent loadings always converges to a best-fitted noisy solution. Since PARAFAC maximally fits the noise part of the data, rank-deficiency is broken, and it causes a noise-induced unique decomposition. The uniqueness due to the presence of noise in rank-deficient cases is an artificial phenomenon called 'surface uniqueness.' The PARALIND model causes non-uniqueness to be revealed, ie, it leads to a different set of profiles in each run. However, it might not give us all the possible solutions. Therefore, there is still a demand for determining all and every possible solution. The aim of this paper is 3-fold: (1) A method is developed for determining feasible regions using the PARALIND model. (2) The surface uniqueness phenomenon is clarified. (3) The effect of interaction matrices in PARALIND as an active constraint is emphasized and discussed in detail using simulated noisy and noise-free two- and three-component data arrays. [ABSTRACT FROM AUTHOR]

Parallel factor analysis (PARAFAC) is believed to be one of the most widely used multiway curve resolution techniques. The superiority of PARAFAC is due to its uniqueness property that is provided under mild assumptions. Unambiguously recovered chemically and physically meaningful profiles by PARAFAC are reliable for quantitative and qualitative application. The essential uniqueness condition of PARAFAC breaks totally or partially in data sets with linearly dependent loadings. PARAFAC uniqueness levels include full uniqueness, partial uniqueness, uni-mode uniqueness, and full non-uniqueness. Although PARAFAC uniqueness conditions are more or less known, they cannot cover the whole of existing uniqueness problems, especially complex rank-deficient systems. The questions investigated here are as follows: Under which conditions is PARAFAC still unique and what is the extent of deterioration of PARAFAC uniqueness by linearly dependent loadings? These are among the most important points in dealing with three-way data arrays with PARAFAC models. Direct visualization of feasible bands using an explicit, well-defined, and trustworthy method is a key feature of our approach to the investigation of uniqueness and recasting partial uniqueness rules in this study. Different simulated examples with different uniqueness levels were designed, and rotational ambiguity was calculated for each case. In this way, the full implication of partial uniqueness was investigated. Direct visualization of feasible bands is beneficial not only for confirmation of previous rules of uniqueness and partial uniqueness but also for development of new theorems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Multivariate curve resolution techniques try to estimate physically and/or chemically meaningful profiles underlying a set of chemical or related measurements. However, the estimation of profiles is not generally unique and it is often complicated by intensity and rotational ambiguities. Constraints as further information of chemical entities can be imposed to reduce the extent of ambiguities. Not only a long list of constraints has been introduced but also some of them can be applied in different ways. Either investigating constraint effects on the extent of rotational ambiguity or how they can be applied during curve resolution can shed light on curve resolution studies. The motivation behind this contribution is to pave the way to a clarification about the closure constraint. Considering simulated equilibrium and kinetic spectrophotometric data sets, different approaches to closure implementation were applied to demonstrate the geometrical explanation of closure constraint and its effect on multivariate curve resolution‐alternating least squares results. Besides, the closure constraint is compared with normalization and it is proved that the closure constraint is a Borgen norm and has the same effect as other Borgen norms in multivariate curve resolution. Finally, to further examine the closure constraint, a real data set was investigated. Investigating constraint effects on the extent of rotational ambiguity or how they can be applied during curve resolution can shed light on the curve resolution studies. The motivation behind this contribution is to pave the way to a clarification about closure constraint. Different approaches to closure implementation were applied to demonstrate the geometrical explanation of closure constraint. Additionally, the closure constraint is compared with normalization, and it is proved that the closure constraint is a Borgen norm. [ABSTRACT FROM AUTHOR]

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. Image 1 • Use of smartphone as a spectrometer (smart spectrometer) and study of the spectral error structure. • Error covariance matrices (ECM) obtained from replicates indicated the presence of heteroscedastic and dependent error. • Use of PCA, MCR-ALS and area of feasible solution (AFS) to resolve the separated error part and clarify the error types. [ABSTRACT FROM AUTHOR]

Aims & Scope: In this research, 8 variable selection approaches were used to investigate the effect of variable selection on the predictive power and stability of CoMFA models., Materials & Methods: Three data sets including 36 EPAC antagonists, 79 CD38 inhibitors and 57 ATAD2 bromodomain inhibitors were modelled by CoMFA. First of all, for all three data sets, CoMFA models with all CoMFA descriptors were created then by applying each variable selection method a new CoMFA model was developed so for each data set, 9 CoMFA models were built. Obtained results show noisy and uninformative variables affect CoMFA results. Based on created models, applying 5 variable selection approaches including FFD, SRD-FFD, IVE-PLS, SRD-UVEPLS and SPA-jackknife increases the predictive power and stability of CoMFA models significantly., Result & Conclusion: Among them, SPA-jackknife removes most of the variables while FFD retains most of them. FFD and IVE-PLS are time consuming process while SRD-FFD and SRD-UVE-PLS run need to few seconds. Also applying FFD, SRD-FFD, IVE-PLS, SRD-UVE-PLS protect CoMFA countor maps information for both fields., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.)

This study is an implementation of a robust jackknife-based descriptor selection procedure assisted with Gram-Schmidt orthogonalization. Selwood data including 31 molecules and 53 descriptors was considered in this study. Both multiple linear regression (MLR) and partial least squares (PLS) regression methods were applied during the jackknife procedures, and the desired results were obtained when using PLS regression on both autoscaled and orthogonalized data sets. Having used the Gram-Schmidt technique, descriptors were all orthogonalized, and their number was reduced to 30. A reproducible set of descriptors was obtained when PLS-jackknife was applied to the Gram-Schmidt orthogonalized data. The simple statistical t-test was applied to determine the significance of the obtained regression coefficients from jackknife resampling.Increasing the sample size, descriptors, based on their information content, were introduced into the model one by one and were sorted. The number of validated descriptors was in proportion with the sample size in the jackknife. The PLS-jackknife parameters, such as sample size and number and number of latent variables in PLS, and the starting descriptor in Gram-Schmidt orthogonalization were investigated and optimized.Applying PLS-jackknife to orthogonalized data in the optimized condition, five descriptors were validated with q²TOT2 ) 0.693 and R² ) 0.811. Compared to the previous reports, the obtained results are satisfactory.