Chemometric Problems Research Articles

On Hidden Rank Deficiency in MCR Problems

ABSTRACTPure component decomposition problems in chemometrics can be classified into rank‐regular and rank‐deficient problems. Rank‐deficient problems are characterized by a spectral data matrix that has a lower rank than the number of chemical species. However, it is possible that there exists rank‐regular factorization of the spectral data matrix, but none of these solutions can be interpreted chemically, and only a solution of the MCR problem with rank deficiency is chemically meaningful. Then we say that the underlying problem suffers from a hidden rank deficiency. In this paper, MCR problems with hidden rank deficiency are introduced and analyzed with several examples for problems of rank 2 and rank 3. The area of feasible solutions is determined with the help of additional constraints on the solution.

Class-specific correction and classification of NIR spectra of edible oils

Classification of NIR spectra is a common problem in chemometrics. An ideal classification model should not only classify spectra into the known defined classes but also detect spectra that do not belong to any of the known classes. On top of this, the classification model should also perform well on spectra with unwanted source of variation (batch effects) obtained under different conditions. Classification of spectra into more distinct classes (different edible oils) is relatively easier than classification of spectra into less distinct classes (purities of oils). It is crucial to eliminate the batch effects while keeping the signal that separates the classes in the spectra effectively.Classification of spectra obtained under different batch conditions is often performed by applying a classification model (PCLDA, SIMCA) on spectra adjusted using calibration transfer methods (PDS, CTCCA and PCPDS). However, the simple calibration transfer models are unable to successfully remove the batch effects due to the heterogenous nature of these effects. In this paper, we propose CSCAC, a class-specific correction and classification technique that simultaneously corrects batch effects and performs both multi-class classification and novel-class detection. It provides a simple but an effect way to use calibration transfer models class-specifically when the class of the test spectra is unknown/to-be determined. We built three different versions of CSCAC models with PDS, PCPDS and CTCCA as base transfer models and benchmarked against commonly used classification methods. We show that class-specific framework is worth articulating explicitly and existing methods benefit from being used via such a framework. We illustrate its classification performance on a 14-edible oil dataset obtained across 5 different batches. We further illustrate its ability to be a quality check model on peanut oil – maize oil mixtures obtained across 25 batches.

A reliable algorithm for calculating stoichiometry parameters in the hard modeling of spectrophotometric titration data

AbstractComputation of binding constants from spectrophotometric titration data is a very popular application of chemometric hard modeling. However, the calculated values are misleading if the correct binding model is not used. Given that many supramolecular systems of interest feature unknown speciation, a priori determination of binding stoichiometry constitutes an important unsolved problem in chemometrics. We present a new and reliable algorithm for accomplishing this task, implemented using a hybrid particle swarm optimization technique. Simultaneous optimization of stoichiometry ratios and binding constants allows the optimal binding model to be calculated in just a few minutes for systems with up to four reactions. Simulated data studies demonstrate that the algorithm finds the correct stoichiometry with up to nine reactions in the absence of noise, including accurately determining species with unusual stoichiometry, such as H2G5. Application to four experimental datasets shows the algorithm is robust to experimental errors for a variety of chemical systems and binding models. This algorithm will facilitate the discovery of complex binding models, increase efficiency in titration analysis, and avert incorrect stoichiometry models, thereby improving the reliability of binding constant information in spectrophotometric titrations.

Review of Variable Selection Methods for Discriminant-Type Problems in Chemometrics

Discriminant-type analyses arise from the need to classify samples based on their measured characteristics (variables), usually with respect to some observable property. In the case of samples that are difficult to obtain, or using advanced instrumentation, it is very common to encounter situations with many more measured characteristics than samples. The method of Partial Least Squares Regression (PLS-R), and its variant for discriminant-type analyses (PLS-DA) are among the most ubiquitous of these tools. PLS utilises a rank-deficient method to solve the inverse least-squares problem in a way that maximises the co-variance between the known properties of the samples (commonly referred to as the Y-Block), and their measured characteristics (the X-block). A relatively small subset of highly co-variate variables are weighted more strongly than those that are poorly co-variate, in such a way that an ill-posed matrix inverse problem is circumvented. Feature selection is another common way of reducing the dimensionality of the data to a relatively small, robust subset of variables for use in subsequent modelling. The utility of these features can be inferred and tested any number of ways, this are the subject of this review.

Development of Multi-Target Chemometric Models for the Inhibition of Class I PI3K Enzyme Isoforms: A Case Study Using QSAR-Co Tool

The present work aims at establishing multi-target chemometric models using the recently launched quantitative structure–activity relationship (QSAR)-Co tool for predicting the activity of inhibitor compounds against different isoforms of phosphoinositide 3-kinase (PI3K) under various experimental conditions. The inhibitors of class I phosphoinositide 3-kinase (PI3K) isoforms have emerged as potential therapeutic agents for the treatment of various disorders, especially cancer. The cell-based enzyme inhibition assay results of PI3K inhibitors were curated from the CHEMBL database. Factors such as the nature and mutation of cell lines that may significantly alter the assay outcomes were considered as important experimental elements for mt-QSAR model development. The models, in turn, were developed using two machine learning techniques as implemented in QSAR-Co: linear discriminant analysis (LDA) and random forest (RF). Both techniques led to models with high accuracy (ca. 90%). Several molecular fragments were extracted from the current dataset, and their quantitative contributions to the inhibitory activity against all the proteins and experimental conditions under study were calculated. This case study also demonstrates the utility of QSAR-Co tool in solving multi-factorial and complex chemometric problems. Additionally, the combination of different in silico methods employed in this work can serve as a valuable guideline to speed up early discovery of PI3K inhibitors.

On ecological aspects of dynamics for zero slope regression for water pollution in Chile

Zero slope regression is an important problem in chemometrics, ranging from challenges of intercept-bias and slope ‘corrections’ in spectrometry, up to analysis of administrative data on chemical pollution in water in the region of Arica and Parinacota. Such issue is really complex and it integrates problems of optimal design, symmetry of errors, stabilization of the variability of estimators, dynamical system for errors up to an administrative data challenges. In this article we introduce a realistic approach to zero slope regression problem from dynamical point of view. Linear regression is a widely used approach for data fitting under assumption of normally distributed residuals. Many times non-normal residuals are observed and also theoretically justified. Our solution to such problem uses the recently introduced inference function called score function of distribution. As a minimization criterion, the minimum information of residuals criterion is used. The score regression appears to be a direct generalization of the least-squares regression for an arbitrary known (believed) distribution of residuals. The score estimation is also distribution sensitive version of M-estimation. The capability of the method is demonstrated by water pollution data examples.

Networkmetrics: multivariate big data analysis in the context of the internet

Multivariate problems are found in all areas of knowledge. In chemistry and related disciplines. The chemometric community was developed in a joint effort to understand and solve problems mainly from a multivariate and exploratory perspective. This perspective is, indeed, of broader applicability, even in areas of knowledge far from chemistry. In this paper, we focus on the Internet: the net of devices that allow an interconnected world where all types of data can be shared and unprecedented communication services can be provided. Problems in the Internet, or, in general, in networking, are not very different from chemometric problems. Yet, they also have their specificities, mainly their typical Big Data nature and the presence of unstructured data. Exabytes of data in the format of text, video, audio, etc. are daily generated in the Internet. Part of these data need to be analyzed for disparate purposes, ranging from the optimization of the communications to cybersecurity and cyberwalfare. We argue that exploratory multivariate analysis is, indeed, useful to tackle these problems and has a role to play in the Big Data arena, currently limited to data mining techniques and visualization analytics. In absence of a better name, we call Networkmetrics the approach of treating Internet problems from the multivariate and exploratory perspective.

Networkmetrics: multivariate big data analysis in the context of the internet

Multivariate problems are found in all areas of knowledge. In chemistry and related disciplines, the chemometric community was developed in a joint effort to understand and solve problems mainly from a multivariate and exploratory perspective. This perspective is, indeed, of broader applicability, even in areas of knowledge far from chemistry. In this paper, we focus on the Internet: the net of devices that allow an interconnected world where all types of data can be shared and unprecedented communication services can be provided. Problems in the Internet or in general in networking are not very different from chemometric problems. Building on this parallelism, we review four classes of problems in networking: estimation, anomaly detection, optimization, and classification. We present an illustrative set of problems and show how a multivariate perspective may lead to significant improvements from state‐of‐the‐art techniques. In the absence of a better name, we call the approach of treating these problems from that multivariate perspective networkmetrics. Networkmetric problems have their own specificities, mainly, their typical Big Data nature and the presence of unstructured data. We argue that multivariate analysis is, indeed, useful to tackle these specificities. Copyright © 2016 John Wiley & Sons, Ltd.

Particle swarm optimization (PSO). A tutorial

Swarm-based algorithms emerged as a powerful family of optimization techniques, inspired by the collective behavior of social animals. In particle swarm optimization (PSO) the set of candidate solutions to the optimization problem is defined as a swarm of particles which may flow through the parameter space defining trajectories which are driven by their own and neighbors' best performances. In the present paper, the potential of particle swarm optimization for solving various kinds of optimization problems in chemometrics is shown through an extensive description of the algorithm (highlighting the importance of the proper choice of its metaparameters) and by means of selected worked examples in the fields of signal warping, estimation robust PCA solutions and variable selection.

A non parametric approach for calibration with functional data

A new nonparametric approach for statistical calibration with functional data is studied. The practical motivation comes from calibration problems in chemometrics in which a scalar random variable Y needs to be predicted from a functional random variable X. The proposed predictor takes the form of a weighted average of the observed values of Y in the training data set, where the weights are determined by the conditional probability density of X given Y. This functional density, which represents the data generation mechanism in the context of calibration , is so incorporated as a key information into the estimator. The new proposal is computationally simple and easy to implement. Its statistical consistency is proved, and its relevance is shown through simulations and an application to data.

Probabilistic model‐based discriminant analysis and clustering methods in chemometrics

In chemometrics, the supervised and unsupervised classification of high‐dimensional data has become a recurrent problem. Model‐based techniques for discriminant analysis and clustering are popular tools, which are renowned for their probabilistic foundations and their flexibility. However, classical model‐based techniques show a disappointing behaviour in high‐dimensional spaces, which up to now have been limited in their use within chemometrics. The recent developments in model‐based classification overcame these drawbacks and enabled the efficient classification of high‐dimensional data, even in the ‘smalln/ largep’ condition. This work presents a comprehensive review of these recent approaches, including regularization‐based techniques, parsimonious modelling, subspace classification methods and classification methods based on variable selection. The use of these model‐based methods is also illustrated on real‐world classification problems in chemometrics using R packages. Copyright © 2013 John Wiley & Sons, Ltd.

Genetic algorithms in chemometrics

This review covers the application of Genetic Algorithms (GAs) in Chemometrics. The first applications of GAs in chemistry date back to the 1970s, and in the last decades, they have been more and more frequently used to solve different kinds of problems, for example, when the objective functions do not possess properties such as continuity, differentiability, and so on. These algorithms maintain and manipulate a family, or population, of solutions and implement a “survival of the fittest” strategy in their search for better solutions. GAs are very useful in the optimization and variable selection in modeling and calibration because of the strong effect of the relationship between presence/absence of variables in a calibration model and the prediction ability of the model itself. This review is not a complete summary of the applications of GAs to chemometric problems; its goal is rather to show the researchers the main fields of application of GAs, together with providing a list of references on the subject. Copyright © 2012 John Wiley & Sons, Ltd.

A tutorial on support vector machine-based methods for classification problems in chemometrics

This tutorial provides a concise overview of support vector machines and different closely related techniques for pattern classification. The tutorial starts with the formulation of support vector machines for classification. The method of least squares support vector machines is explained. Approaches to retrieve a probabilistic interpretation are covered and it is explained how the binary classification techniques can be extended to multi-class methods. Kernel logistic regression, which is closely related to iteratively weighted least squares support vector machines, is discussed. Different practical aspects of these methods are addressed: the issue of feature selection, parameter tuning, unbalanced data sets, model evaluation and statistical comparison. The different concepts are illustrated on three real-life applications in the field of metabolomics, genetics and proteomics.

How to simulate normal data sets with the desired correlation structure

The Cholesky decomposition is a widely used method to draw samples from multivariate normal distribution with non-singular covariance matrices. In this work we introduce a simple method by using singular value decomposition (SVD) to simulate multivariate normal data even if the covariance matrix is singular, which is often the case in chemometric problems. The covariance matrix can be specified by the user or can be generated by specifying a subset of the eigenvalues. The latter can be an advantage for simulating data sets with a particular latent structure. This can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their applicability; checking their robustness when the hypothesized properties fail; or generating data from multi-stage or multi-phase processes.

Multi-core computing: A novel accelerating method for chemometrics calculation

The higher speed is the eternal pursuit of any chemometric algorithm. In order to take full advantage of the multi-core processor's computing resources (the prevailing current of personal computer) and accelerate the time-consuming algorithms in chemometrics, a novel multi-core computing method is introduced. Leave-one-out cross-validation is taken as an example to show the powerful capability of the multi-core computing. The comparison results show that the execution time drops rapidly with the increasing number of computing cores, which demonstrates that the multi-core computing is a promising tool for solving computing-intensive and data-intensive problems in chemometrics.

Artificial neural networks in chemometrics: History, examples and perspectives

Artificial neural networks (ANNs) are non-linear computational tools suitable to a great host of practical application due to their flexibility and adaptability. However, their application to the resolution of chemometric problems is relatively recent (early 1990s). In this communication, different artificial neural networks architectures are presented and their application to different kinds of chemometric problems (mainly classification and regression) is discussed by means of examples taken from the authors' experience, stressing the pros and cons of ANNs with respect to traditional chemometric techniques.

Counter-propagation neural networks in Matlab

The counter-propagation neural networks have been widely used by the chemometricians for more than fifteen years. This valuable tool for data analysis has been applied for solving many different chemometric problems. In this paper the implementation of counter-propagation neural networks in Matlab environment is described. The program presented here is an extension of Self-Organizing Maps Toolbox for Matlab that is not widely used by chemometricians. This program coupled with the excellent visualization tools available in Self-Organizing Maps Toolbox and with other valuable functions in this environment could be of great interest for analysis of chemical data. The use of the program is demonstrated on the development of the regression and classification models.

An adapted version of the element-wise weighted total least squares method for applications in chemometrics

The Maximum Likelihood PCA (MLPCA) method has been devised in chemometrics as a generalization of the well-known PCA method in order to derive consistent estimators in the presence of errors with known error distribution. For similar reasons, the Total Least Squares (TLS) method has been generalized in the field of computational mathematics and engineering to maintain consistency of the parameter estimates in linear models with measurement errors of known distribution. In a previous paper [M. Schuermans, I. Markovsky, P.D. Wentzell, S. Van Huffel, On the equivalance between total least squares and maximum likelihood PCA, Anal. Chim. Acta, 544 (2005), 254–267], the tight equivalences between MLPCA and Element-wise Weighted TLS (EW-TLS) have been explored. The purpose of this paper is to adapt the EW-TLS method in order to make it useful for problems in chemometrics. We will present a computationally efficient algorithm and compare this algorithm with the standard EW-TLS algorithm and the MLPCA algorithm in computation time and convergence behaviour on chemical data.

A generalized boosting algorithm and its application to two-class chemical classification problem

Boosting is one of the most important recent developments in classification methodology. It can significantly improve the prediction performance of any single classification algorithm and has been successfully applied to many different fields including problems in chemometrics. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data, and then taking a weighted majority vote of the sequence of classifiers thus produced. In this paper, we proposed a generalized boosting algorithm via Bayes optimal decision rule. Using Bayes optimal decision rule, we adjust the weights of the sequence of classifiers in the voting process of boosting algorithm. The two types of errors are introduced into the generalized boosting and make the voting process more sensible. Meanwhile, the weights of the training samples are also correspondingly adjusted according to some criterion. The generalized boosting is applied to the binary classification for chemical data. Experimental results show that it can improve the predict accuracy compared with AdaBoost algorithm especially when the difference between the two types of errors for classification is large.

Application of boosting to classification problems in chemometrics

Application of boosting to both two-class and multi-class classification problems are studied. Five real chemical data sets are used. Each data is randomly divided into two subsets, one for training and the other for prediction. For two-class classification, each data is separated into a high response level class and a low response level class according to a threshold value. As a result, three data sets, wheat data, cream data and HIV data, show that boosting using classification and regression trees (CART) as a base learner may decrease the misclassification rate in prediction with respect to using a single CART. However, boosting for green tea data indicates that overfitting may occur when boosting is applied. For the chromatographic retention data, boosting performs worse than a single CART. The cream data and the HIV data are also used for multi-class classification. Both data sets demonstrate that boosting performs better than CART in multi-classification. Variable importance analysis suggests that the improvement made by boosting may be due to the use of more variables, which give more information on special types of samples in the training data.