Interpretive optimization criteria

Typically, resolution diagrams in MLC are complex, with several local maxima, frequently denoting interaction between factors. For this reason, reliable optimal conditions require considering all factors simultaneously, by applying an interpretive optimization strategy (i.e., based on the description of the retention behavior and peak shape of solutes). In this task, the product of free peak areas or purities has proved to be the best optimization criterion. An interactive computer program is available to obtain the best separation conditions in... 

The selection of cluster number, which is generally not known beforehand, represents the primary performance criterion. Optimization of performance therefore requires trial-and-error adjustment of the number of clusters. Once the cluster number is established, the neural network structure is used as a way to determine the linear discriminant for interpretation. In effect, the RBFN makes use of known transformed features space defined in terms of prototypes of similar patterns as a result of applying /c-means clustering. 

In contrast to PCA which can be considered as a method for basis rotation, factor analysis is based on a statistical model with certain model assumptions. Like PCA, factor analysis also results in dimension reduction, but while the PCs are just derived by optimizing a statistical criterion (spread, variance), the factors are aimed at having a real meaning and an interpretation. Only a very brief introduction is given here a classical book about factor analysis in chemistry is from Malinowski (2002) many other books on factor analysis are available (Basilevsky 1994 Harman 1976 Johnson and Wichem 2002). 

Table Vtll. Simultaneous bensity and Temperature Optimization via an Interpretive (Window Diagram) Approach Criterion threshold separation factor (CRF-4, equation 9) Optimum conditions density, 0.19 g/mL temperature, 104 °C Chromatogram Figure 10 ...

Figure 8.28 is a scatter plot of the first two rotated PC scores obtained from a PCA analysis of the NIR spectra of polyethylene blend films, after rotation was done to improve interpretability. In this example, it was determined that three PCs were optimal for the PCA model, and the rotated PCs one, two, and three explain 46.67, 49.25, and 2.56% of the variation in the NIR spectra, respectively. Although the higher explained variance of the second rotated PC might seem anomalous based on the criterion that PCA uses explained variance to determine each PC, one must be reminded that these explained variances refer to rotated PCs, rather than the original PCs. There are two interesting things to note about this plot ... 

Although the value of Rs for a given pair of peaks can be quickly transferred from one column to another by using the proportionality of Rx and Vn, this is not the case for the threshold criterion of eqn.(4.23). The problem is that if we know the boundaries of the area for which Rs min > 1 using a column of 10,000 plates, we only know the boundaries of the area for which Rs min > 0.5 for a column with 2,500 plates. We do not know what the boundaries for Rs min > 1 are in the latter case, because we have no information on how the value of Rs min changes with variations in the parameter settings. Only if the variation of the capacity factors as a function of the relevant parameters is known, can the boundaries of the area in which the resolution is adequate be calculated for different columns with different numbers of theoretical plates. Optimization methods in which this is the case (so-called interpretive methods ) will be discussed in section 5.5. 

A first MCDM approach is Pareto optimality. An experiment is considered Pareto-optimal when no other experiment exists with a better result on one criterion without having a worse result on another. This method mostly is used when only two responses are examined, because of the easy graphical interpretation. Theoretically, it can also be applied for more than two responses, although the (graphical) interpretation then is less straightforward. Moreover, the more responses are examined, the more unlikely it becomes that one experiment will dominate another for all considered responses, which makes this method less useful. It also should be noticed for the two-response case that a Pareto-optimal point is not always representing a practically suitable optimum. 

The detection limit indicates the performance of an instrument at low analyte concentrations. This indication may be used as a guide to instrument optimization, as a gauge of the suitability of an instrument for a particular application, or as a criterion for the interpretation of low concentration measurements. This paper concentrates on the latter use of detection limits and expands the discussion to include all aspects of statistical inference on low concentration measurements. In this case, the use of the detection limit is confined to the measurements in question and to the study at hand. The use of detection limits for instrument optimization and for suitability judgments requires a broader perspective that covers the various conditions under which the instrument might be used. 

A classical approach to this problem involves developing a se wence of models, as shown in Fig. 2. The first step in this chain, labelled 1 in the figure, is the development of a fundamental model Mf describing the dynamic interplay between dominant chemical and physical process phenomena. This model is optimized with respect to the first two model validity criteria— ability to predict process behavior accurately and physical interpretability—and advances in model development tools are improving the quality of fundamental models with respect to the fourth criterion (ease of development). Because their complexity is determined by process details, however, fundamental models typically suffer badly with respect to the third criterion they are not directly compatible with most model-based control strategies. 

The MS database system MassLib uses a composite similarity criterion containing the similarity criterion Sj together with measures for the number and intensity sums of peaks that are common or not in both spectra. The algorithm has been optimized to give good results for identification as well as for interpretation. 

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