Exploratory analyses

Some of the most useful applications of chemometric methods involve the extraction of hidden information in large, complex databases. At first glance, such applications might not seem to be relevant for PAT, until one considers the following  

PAT is called upon to support not only manufacturing operations, but also product and process research and development efforts  

The highly empirical nature of chemometric tools can lead to customer suspicion regarding the efficacy of chemometric models and 

Some PAT applications allow for, or require, analyzer hardware optimization. 

With these considerations in mind, it becomes clear that the information extraction capability of chemomet-rics can be quite useful in several PAT-relevant situations, especially during the research and development phase of a project, or when one is trying to improve customer confidence in the capability of a calibration. As a result, a short discussion of several common exploratory tools will be made here. 

Many of the chemometrics tools mentioned above can be used to extract valuable information about sample chemistry, the measurement system, as well as process dynamics. Such information can be very useful in a process analytical environment, where the emphasis is usually on developing and automating on-line quantitative analyses. Several different means for information extraction are discussed below. 

When one builds a quantitative model using PCR or PLS, one is often not aware that the model parameters that are generated present an opportunity to learn some useful information. Information extracted from these model parameters cannot only be used to better understand the process and measurement system, but also lead to improved confidence in the validity of the quantitative method itself. 

The PC scores can be used to assess the relationships between different samples in the model. If this information is combined with known class information about the samples, an assessment of the effectiveness of the analytical method for distinguishing between classes can be made. Furthermore, the scores can be used to detect trends in the samples that might not be expected. It is common to plot PC scores using a two-dimensional scatter plot, where the axes represent different PC numbers. 

Blend composition, in % HDPE Number of replicate samples analyzed 

The PC loadings can be used to assess relationships between different variables in the model, as well as help explain the fundamental basis of the phenomena explained by the PCs. More specifically, if one looks at the loadings for the dominant PCs in the model, they can be used to detect general correlations between X-variables. For this purpose, they are often plotted as two-dimensional scatter plots, where each axis corresponds to a different PC number. An example of such a loading scatter plot for the polyethylene data 

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Reilly, T.F. Jenkins, R.P. Murrmann, D.L. Legget R. Barrierra, Exploratory Analysis of Vapor Impurities from TNT, RDX Composition B , Special Rept 194, Cold Regions Res Eng Lab, US Army Corps of Engineers, Hanover, NH (Oct 1973) 59) J.J. Rocchio... 

Aschengrau A, Coogan PE, Quinn MM, et al. 1998. Occupational exposure to estrogenic chemicals and the occurrence of breast cancer An exploratory analysis. Am J Ind Med 34 6-14. 

Rather than finding the exact location of the single feasible hyperrectangle that optimizes i/f (X), our primary goal is to conduct an exploratory analysis of the decision space, leading to the definition of a set of particularly promising solutions, X, to be presented to the decisionmaker. 

A. de Juan, B. van den Bogaert, F. Cuesta Sanchez and D.L. Massart, Application of the needle algorithm for exploratory analysis and resolution of HPLC-DAD data. Chemom. Intell. Lab. Syst.,33 (1996) 133-145. 

Deal, M. (1990), Exploratory analysis of food residues from prehistoric pottery and other artifacts from eastern Canada, SAS Bull. 13(1), 6-12. 

Currie, L. A., Polach, H. A., Exploratory Analysis of the International Radiocarbon Cross-Calibration Data Consensus Values and Interlaboratory Error, Proceedings of the 10th International Radiocarbon Conference, Radiocarbon. 22, 933... 

Two main groups of exploratory analysis may be identified representation techniques and clustering techniques. 

Depending on the PAT application, there could be additional, or different, objectives to the experiment. For example, one might not want to build a quantitative regression model for an on-line analyzer, but rather perform an exploratory analysis to identify which of many design variables has the greatest affect on the analyzer response, hi this case, a set of tools called screening designs [22] can be quite useful. 

D. Hoaglin, F. Mosteller, and J. Tuke>-, Understanding Robust and Exploratory Analysis, Wiley, New York, 1983. 

Clustering is a branch of exploratory analysis able to provide answers about the presence of groupings among objects or variables, by means of a similarity measurement (Vandeginste et al., 1998). The similarity among two objects is defined as an inverse fimction of their distance the more two objects are distant, the less they are similar. Several metrics may be used to evaluate the distance D between two objects i and j in a n-dimensional space. The most common are... 

Another type of ANNs widely employed is represented by the Kohonen self organizing maps (SOMs), used for unsupervised exploratory analysis, and by the counterpropagation (CP) neural networks, used for nonlinear regression and classification (Marini, 2009). Also, these tools require a considerable number of objects to build reliable models and a severe validation. 

The rule of the K nearest objects, KNN, has been used in classification problems, in connection and comparison with other methods. Usually KNN requires a preliminary standardization and, when the number of objects is large, the computing time becomes very long. So, it appears to be useful in confirmatory/exploratory analysis (to give information about the environment of objects) or when other classification methods fail. This can happen when the distribution of objects is very far from linear, so that the space of one category can penetrate into that of another, as in the two-dimensional example shown in Fig. 28, where the category spares, computed by bayesian analysis or SIMCA, widely overlap. 

Table 8.9 A summary of the HDPE/LDPE blend films used to demonstrate exploratory analysis methods...

The most important method for exploratory analysis of multivariate data is reduction of the dimensionality and graphical representation of the data. The mainly applied technique is the projection of the data points onto a suitable plane, spanned by the first two principal component vectors. This type of projection preserves (in mathematical terms) a maximum of information on the data structure. This method, which is essentially a rotation of the coordinate system, is also referred to as eigenvector-projection or Karhunen-Loeve- projection (ref. 8). 

EIN SIGHT Infometrix, 2200 Sixth Ave. 833, Seattle, Wash. 98121, USA 300. Exploratory analysis of multivariate data, graphics-oriented (ref. 18). 

The information obtained in the FSIW-EFA exploratory analysis is used in the resolution step. The total number of compounds in the three-way data set has been found to be equal to three (active, excipient, and unknown). The iterative optimization process starts with a matrix ST containing the initial estimates found by... 

Heres, S., Davis, J., Maino, K., Jetzinger, E., Kissling, W.,. Leucht, S. 2006, Why olanzapine beats risperidone, risperidone beats quetiapine, and queti-apine beats olanzapine an exploratory analysis of head-to-head comparison studies of second-generation antipsychotics, Am.f.Psychiatry, vol. 163, no. 2, pp. 185-194. 

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