Qualitative discriminant analysis

H. Mark, Qualitative discriminant analysis. In Handbook of Near-Infrared Analysis, 2nd edition, D. Bums and E.W. Ciurczak (eds), Marcel Dekker, New York, 351-362, 2001. 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

The experimental mechanistic study of the anodic cyclization reactions requires values for the variation of the peak potential (Ep) in LSV with the sweep rate (v), the concentration of substrate (C) and the concentration of added base (B). The plots of dEp/dlogv, dEp/dlogC, and dEp/dlogB provide an effective tool for qualitative mechanistic analysis. The diagnostic criteria developed for discrimination between the various possible mechanisms [5] and adopted for oxidative cyclizations are presented in Table 1. 

The pattern of egg rejection very closely matched the variations in the pattern of the hydrocarbon profiles present on the egg surfaces. Eggs of highly fertile queens showed profiles that were qualitatively different to those of eggs laid by workers and weakly fertile queens (Endler et al., 2004, 2006 Figure 13.1). On the other hand, profiles of eggs laid by weakly fertile queens and workers did not show qualitative differences. Nevertheless, weak quantitative differences exist between the profiles of eggs laid by weakly fertile queens and workers that, however, do not relate to type of egg-layer or fertility according to the classification pattern of a discriminant analysis (Endler et al., 2006). 

For analysis of more complicated tablet matrices, it is unlikely that training sets of 14 or fewer samples would suffice in the development of robust models for quantitation or qualitative discrimination. Considering a typical tablet with, say,... 

In two papers, Ritchie et al. [29,30] described an approach for performing qualitative NIR analysis of clinical samples with a concern for cGMPs (current good manufacturing practices). Since clinical lots are often ad hoc formulations, it is difficult to generate a discriminant equation prior to the actual clinical trial. Ritchie developed a procedure whereby equa-... 

Schlich et al. (1987) proposed a new approach to selecting variables in principal component analysis (PCA) and getting correlations between sensory and instrumental data. Among other studies, Wada et al. (1987a,b) evaluated 39 trade varieties of coffee by coupling gas chromatographic data with two kinds of multivariate analysis. The objective classification was compared with the sensory data (cup test), directly or after statistical treatment. The results were concordant. Murota (1993) used qualitative sensory data to interpret further the results of GC data and canonical discriminant analysis. He could thus suggest which were the components responsible for the flavor characteristics in different coffee cultivars. 

Discriminant analysis (Figure 31) [41,487, 577 — 581] separates objects with different properties, e.g. active and inactive compounds, by deriving a linear combination of some other features e.g. of different physicochemical properties), which leads to the best separation of the individual classes. Discriminant analysis is also appropriate for semiquantitative data and for data sets, where activities are only characterized in qualitative terms. As in pattern recognition, training sets are used to derive a model and its stability and predictive ability is checked with the help of different test sets. 

NIR instruments may not only be calibrated for quantitative analysis, but they may also be trained for qualitative purposes. This process is usually termed discriminant analysis. The criteria noted previously for establishing quantitative calibrations with minimum prediction error are equally applicable to discriminant calibration sets. 

In 1984, Mark introduced the Mahalanobis distance in an algorithm for discriminant analysis of raw materials. The theory behind the software was described in a paper by Mark and Turmell [21] and first applied to pharmaceuticals by Ciurczak [22]. With the advent of 100% testing of incoming raw materials, qualitative analysis of raw materials by NIR became popular quickly. 

R. Franke and W. Meisske, Acta Biol. Med. Germ., 35, 73 (1976). Discriminant Analysis of Structure-Activity Relationships of Qualitative Biological Data Virostatic Action of Isatin-B-isothi osemicarbazones. 

In the case of qualitative analysis, the moisture content of the samples is the most important factor that influences the NIR spectra. If there are differences in moisture content among the groups of samples, each group can be easily classified. To avoid this possibility, it is better to perform a moisture control of the samples. In a study on the classification of normal and aged soybean seeds by NIR discriminant analysis, the moisture content of each single kernel was controlled in a desiccator with silica gel at room temperature until each one had a constant moisture content of 14.6% (11). 

In near-infrared spectroscopy (NIRS), as we have seen in earlier chapters, one teaches the instru-ment/computer system what to look for in a given type of sample, then expects the hardware/software combination to produce valid answers when it is presented with unknown samples of the same type. But what kind of answers are we seeking Usually, they are quantitative answers, in other words, how much of substance XYZ is present in the sample. Occasionally we use what is called discriminant analysis to obtain a qualitative answer, in other words, is this sample A, B, C, or none of these ... 

However, the current implementations of the discriminant analysis approach to qualitative analysis via NIR spectroscopy use Mahalanobis distances rather than linear discriminant functions because of their other characteristic Linear discriminant functions do not permit as straightforward a means of detecting outliers and samples not in the training set as Mahalanobis distances do, in addition to other advantages that will be considered further on. 

Near-infrared reflectance analysis is a useful technique for characterizing textile raw materials, fiber, yarns, and fabrics. It is a nondestructive quantitative analysis that is simple to use and allows rapid testing of the sample. Its ability to measure multiple components of the sample simultaneously and eliminate extensive sample preparation are major advantages of NIRA in the characterization of textile materials. Many innovative mathematical treatments, for example, discriminant analysis and spectral reconstruction, have been developed by instrument manufactures and software companies. These instruments not only aid in the quantitative analysis of the data but also allow morphological investigations of fibers and yarns and rapid, qualitative identification of specific sample sets. 

When many different types of products are being analyzed, a practical technique often utilized is to combine qualitative analysis with quantitative analysis. First, the unknown are classified by qualitative analysis, in other words, discriminant analysis [35,77], Cascade software [78] automatically classifies a sample using discriminant analysis and steps to the proper calibration for quantitative... 

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