Chemometrics projections

Fig. 1-2. A generic holistic strategy for a chemometric project (according to [GELADI, 1995])...

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

PLS has been introduced in the chemometrics literature as an algorithm with the claim that it finds simultaneously important and related components of X and of Y. Hence the alternative explanation of the acronym PLS Projection to Latent Structure. The PLS factors can loosely be seen as modified principal components. The deviation from the PCA factors is needed to improve the correlation at the cost of some decrease in the variance of the factors. The PLS algorithm effectively mixes two PCA computations, one for X and one for Y, using the NIPALS algorithm. It is assumed that X and Y have been column-centred as usual. The basic NIPALS algorithm can best be demonstrated as an easy way to calculate the singular vectors of a matrix, viz. via the simple iterative sequence (see Section 31.4.1) ... 

Another recent tool has been developed within the ORCHESTRA project. The tool keeps into account both the chemometric information and the toxicity predictions done by the model, and in particular what kind of errors have been done by the model. It applies to the CAESAR QSAR models. Furthermore, this tool is based not only on the a priori data and information, as the other approaches, but also on the a posteriori result of the model. The user knows if the model can or cannot be used for a certain compound. In some cases a warning is given, recommending expert opinion. In all cases the reasons for the reliability is given, and it can be evaluated in a transparent way. 

For practical computation the software environment R is used. R is a powerful statistical software tool, it is freeware and can be downloaded at http //cran.r-project. org. Throughout the book we will present relevant R commands, and in Appendix 3 a brief introduction to R is given. An R-package chemometrics has been established it contains most of the data sets used in the examples and a number of newly written functions mentioned in this book. 

Model deployment logistics might not be academically interesting, but they are absolutely critical for project success. The most effective method in the world, developed using state of the art modehng methods, is worthless unless it can be deployed in an effective, safe and sustainable manner. Unfortunately, though, the deployment landscape of chemometrics in PAT can vary widely between applications, and thus the details of model deployments can vary widely as well. Nonetheless, this section wiU attempt to provide a brief summary of the more common deployment issues that arise in PAT applications. 

Ultimately, the effectiveness of a model lies in its ability to provide usefnl and timely information to the customers, which for PAT applications are often process engineers, operators and manufacturing operations personnel. Therefore, one must also consider how best to integrate the chemometric models with the existing data handling and control system. Below are several issnes in this area that are commonly experienced in PAT projects ... 

Based on my experiences, and experiences from my colleagues, there are several issues that seem to recur in PAT projects, and some that are unique to those that involve chemometrics ... 

With these principles in mind, and the tools at your disposal, you are ready to put chemometrics to work for your PAT projects. 

One chemometric method used to monitor mixing involves comparing the spectrum for the unknown sample with that for one assumed to be homogeneous via the so-called conformity index , which is calculated by projecting the spectrum for the unknown sample onto the wavelength space of the spectrum or mean of spectra for the homogeneous sample. This procedure is similar to that involving the calculation of distances in a principal component space. 

The simplest and most widely used chemometric technique is Principal Component Analysis (PCA). Its objective is to accomplish orthogonal projection and in that process identify the minimum number of sensors yielding the maximum amount of information. It removes redundancies from the data and therefore can be called a true data reduction tool. In the PCA terminology, the eigenvectors have the meaning of Principal Components (PC) and the most influential values of the principal component are called primary components. Another term is the loading of a variable i with respect to a PQ. 

Unfortunately, it is this writer s opinion that, considering the voluminous publications on chemometrics applications, the number of actual effective process analytical chemometrics applications in the field is much less than expected. Part of this is due to the overselling of chemometrics during its boom period, when personal computers (PCs) made these tools available to anyone who could purchase the software, even those who did not understand the methods. This resulted in misuse, failed applications, and a bad taste with many project managers (who tend to have long memories...). Part of the problem might also be due to the lack of adequate software tools to develop and safely implement chemometric models in a process analytical environment. Finally, some of the shortfall might simply be due to lack of qualified resources to develop and maintain chemometrics-based analytical methods in the field. 

The above facts underscore the critical need for documentation of chemometric model building. With sufficient documentation in place, the user is able to continue working on model development on an interrupted project in a time-efficient manner, and without duplicating prior effort. Documentation on the final model(s) that is currently being used on-line can also serve to provide necessary information for satisfying regulatory agencies such as ISO and the FDA, provided that they contain the required information about the models. 

Most of these issues can be addressed through interpersonal skills, which are not the subject of this chapter. However, the staling process of chemometric models can be addressed by performing three important tasks during the project (1) publicize the limitations of your models as soon as you are aware of them, (2) do the hard work early on (experimental designs for calibration, collection and analysis of many samples) in order to avoid embarrassments through model extrapolations, and (3) keep an eye on your methods as they are operating, and update/adjust them promptly. 

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