Discriminating power

The discriminating power (DP) of a set of chromatographic systems is defined as the probability of identifying two randomly selected solutes in at least one of the systems. For k chromatographic systems in which N compounds are investigated, the DP is given by Equation 4.33 [18] ... 

When we consider the multivariate situation, it is again evident that the discriminating power of the combined variables will be good when the centroids of the two sets of objects are sufficiently distant from each other and when the clusters are tight or dense. In mathematical terms this means that the between-class variance is large compared with the within-class variances. 

In SIMCA, we can determine the modelling power of the variables, i.e. we measure the importance of the variables in modelling the elass. Moreover, it is possible to determine the discriminating power, i.e. which variables are important to discriminate two classes. The variables with both low discriminating and modelling power are deleted. This is more a variable elimination procedure than a selection procedure we do not try to select the minimum number of features that will lead to the best classification (or prediction rate), but rather eliminate those that carry no information at all. 

Obviously, it is very important that the next experiment has maximum discriminating power. Let us illustrate this point with a very simple example where simple common sense arguments can lead us to a satisfactory design. Assume that we have the following two rival single-response models, each with two parameters and one independent variable ... 

Figure 12.1 The two rival models can describe equally well data taken near x2 andx4, whereas data taken near X/ or x3 or particularly xs will have a high discriminating power.

We have several options in terms of designing the next experiment that will have the maximum discriminating power among all the above four rival models ... 

As seen in Tables 12.7 and 12.8 when ae is in the range 0.001 to 0.2 g/L the experiment with the square wave input has a higher discriminating power. As expected the x2-test is overall more powerful since ae is assumed to be known. 

Although the feasibility of direct probe MS for the analysis of additives in complex polymeric matrices has been demonstrated (Section 6.4), application is limited, difficult and requires above-average mass-spectroscopic expertise. Direct desorption in the MS probe is usually limited to screening of volatile components. Direct multicomponent spectroscopic analysis has other hurdles to overcome (UV/VIS lack of spectral discrimination IR/R functional-group recognition only, with no discriminative power for additives with similar functionalities NIRS unsuitable for R D problems NMR sensitivity). 

Total specimens for the seven reference units are given, by site provenience, in Table 3. The units are represented in five dimensional discriminant space, the coordinates for the first two dimensions being shown in figure 4. These two vectors account for 72 percent of the total discriminant power. For convenience, approximate territorial lines have been added to the plot. Apparently representing the compositional pattern of locally made Palenque pottery, units 1 and 2 are enclosed within a single territorial boundary. Less well represented but, as will be seen, of considerable interest for the incesario problem, is unit 7, which relates primarily to the site of Xupa. Observable separation of units 3, 4, and 5 is possible only when utilizing additional discriminant functions beyond the first and second. In... 

Moreover, differentiation of the 38 segments of an SP-chip brought about by the temperature and membrane thickness gradient has proved to provide high quality gas discrimination power. An analysis of the signal patterns obtained for some gases present in the early stages of fires is shown in Fig. 3.30. Prior to the... 

In order to investigate the discrimination power of the gradient microarray regarding the changes in air composition, a signal pattern analysis was performed... 

The application of various mathematical statistical methods such as the information content derived from Shanon s equation, calculation of discriminative power and formation of cluster dendograms indicated that the best separation can be achieved by mobile phases 2 and 10 [116]. 

Improved LIF sensing discrimination power is required for sample matrices that contain multiple fluorophores with similar spectral emission properties or when background emission is problematic. Distinguishing among airborne bioagent hazards and common emissive interferants (albuminous, epithelium, and cellulous materials as well as aromatic hydrocarbons), is a prime example where higher selective detection is required. This can be achieved via the lifetime properties of each fluorophore, by an optode approach or both. 

However, SMV has a relatively low discriminating power, which may require the use of near-unity thresholds in order to distinguish very similar products. It can also result in ambiguous identification of batches of the same substance with different physical characteristics (e.g. samples of the same product with different grain sizes can have very similar correlation coefficients and may be confused) or different substances with high chemical similarity. In these cases, cascading libraries, as previously discussed, can be used. 

Distance-based methods possess a superior discriminating power and allow highly similar compounds (e.g. substances with different particle sizes or purity grades, products from different manufacturers) to be distinguished. One other choice for classification purposes is the residual variance, which is a variant of soft independent modeling of class analogy (SIMCA). 

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