Journal of Chemometrics

From its birth approximately a century ago, latent variable analysis has evolved to become the preferred, and more and more frequently, the only possible road to meaningful extraction of information from data in many different application areas. Furthermore, it represents a formal backbone to experience-based learning, that is, co-variance detection and induction, for complex systems. This work describes the evolution, the nature and possibilities of the latent variable approach.

This paper overviews the flexibility of Tikhonov regularization (TR) to form a spectral calibration and maintain it over time. The TR variants can be used in full wavelength modes or with wavelength selection (bands and/or individual for sparse models). Also, included is a TR design that minimizes the effect of the standardization set composition, that is, reduces the effect of an outlier. On-going work that removes all reference samples from the TR framework is also described.

Modern chemistry, biology and medicine have demanded new chemometrics methods that focus more on model interpretation and transparency rather than the traditional emphasis on predictive capacity. Important contributions in this area have been the development of orthogonal based methods, e.g. OSC and OPLS. Here, we provide a conceptual explanation of advantages using orthogonal based methods in multivariate classification and calibration. We also report that orthogonal methods can improve prediction capacity by knowledge acquired through orthogonal inspection.

Bi-modal OnPLS extends the OnPLS method by allowing arbitrary relationships in both columns and rows and by extracting orthogonal variation in both columns and rows. The predictive score vectors exhibit maximal covariance and correlation in the column space, and the predictive loading vectors exhibit maximal correlation in the row space. Two synthetic data sets and one sensory data set were investigated. Bi-modal OnPLS greatly improved the intercorrelations between loadings and scores and facilitated interpretation of the predictive and orthogonal components.

In this paper, we demonstrate how to take advantage of the large number of spatial samples provided by commercial multispectral RGB imagers. We investigate the possibility to use various multidimensional histograms and probability distributions for decomposition and predictive models. We show how these methods can be used in an example using images of different Skyros wall lizards and demonstrate improved performance in prediction of color morph compared with traditional parameterization techniques of spatial variance.

Nowadays, chemometric applications often have tens of thousands of variables. Traditional tools such as principal component analysis or hierarchical clustering are often not optimal for such high rank and information-dense data sets. Coclustering is the tool of choice when only a subset of variables is related to a specific grouping among objects. Hence, coclustering allows a select number of objects to share a particular behavior on a select number of variables.

Multivariate data sets that contain non-uniform (heteroscedastic) measurement error variances create special problems for conventional exploratory data analysis techniques. When information about the error structure is known, the performance of subspace projection methods can be improved. Important considerations related to noise reduction, preprocessing (centering, scaling), subspace estimation, error propagation, and data projection are described for such cases, and the concept of partial transparency projection is introduced. An application to a DNA microarray study is presented.

Robust calibration methods have been developed to protect the analysis against the harmful influence of possible outliers in the data. We propose several robust preprocessing methods as well as robust measures of the root mean squared error of prediction. To select the optimal preprocessing method, we use the desirability index, which is a concept from industrial quality control. We illustrate our procedure through the analysis of a data set containing near-infrared measurements of samples of animal feed.

The PARAFAC (parallel factor analysis) model is a very popular and widely used method to explore multiway data. Because it is well known that the PARAFAC model is very sensitive to outliers, a robust alternative has already been proposed in literature. In this paper, we present an approach to perform PARAFAC on data that contain both outlying cases and missing elements. A simulation study and a real data analysis show the good performance of our methodology.

The interest in process analytical technology (PAT) indicates that this approach is not a fashionable phenomenon but a response to the demands of modern manufacturing process. PAT approach could become a new industrial paradigm that is broadly applicable as a new manufacturing model and goes far beyond pharmaceutical (or related) areas. The role of chemometrics in PAT solutions development is presented in the review on the basis of publications from 1993 to 2011.

The presented method of compensation for random error for two-step processes makes is possible to decrease the cost, obtain lower variation in the final output and still satisfy specific quality constraints. The method utilizes intermediated measurements between the steps when setting control variables in the second step. The paper compares optimal solutions by this method to optimal solutions by methods where all variables are fixed before the process is starting.

We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non-negative states. We motivate the methodology using a real data chemical engineering example and show that a variety of restrictive constraints from earlier analyses do not address the problem of interpretability. Our proposed method estimates parameters using a smoothing based relaxation of the model to enforce interpretability of the observed and unobserved system states.

An adequate sampling interval can be determined for spectral measurements when utilizing a multivariate extension of variography by applying score vectors as independent sources of uncertainty. The error found this way depends on the variance in the spectra but also on the number of utilized score vectors. This approach is illustrated with a crystallization process continuously followed with an attenuated total reflectance Fourier transform infrared instrument.

Multilevel methods, such as multilevel simultaneous component analysis, greatly enhance the interpretation of large sets of batch process data by separating the between-run and within-run variation. Using a multilevel approach in batch process monitoring greatly reduces the occurrence of false alarms that are caused by trivial variations and process changes that were made on purpose. Relevant phenomena that are masked by larger but uninteresting sources of variation if standard methods are used can often be detected as well.

The first applications of Genetic Algorithms (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. 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.