Other Discriminant Classification Methods

So, the chemical direction discriminates Barolo from the other wines, the physical direction discriminates between Barbera and Grignolino. The classification ability of the selected variables is very good and probably some variables can be cancelled without noticeable loss of separation of the categories. Therefore, a small figure shows the relevant information given by a data matrix of 178 rows and 8 columns. Anyway, classification methods and feature selection methods will not modify the quality of these conclusions. 

Discriminant analysis (DA) performs samples classification with an a priori hypothesis. This hypothesis is based on a previously determined TCA or other CA protocols. DA is also called "discriminant function analysis" and its natural extension is called MDA (multiple discriminant analysis), which sometimes is named "discriminant factor analysis" or CD A (canonical discriminant analysis). Among these type of analyses, linear discriminant analysis (LDA) has been largely used to enforce differences among samples classes. Another classification method is known as QDA (quadratic discriminant analysis) (Frank and Friedman, 1989) an extension of LDA and RDA (regularized discriminant analysis), which works better with various class distribution and in the case of high-dimensional data, being a compromise between LDA and QDA (Friedman, 1989). 

Besides the classical Discriminant Analysis (DA) and the k-Nearest Neighbor (k-NN), other classification methods widely used in QSAR/QSPR studies are SIMCA, Linear Vector Quantization (LVQ), Partial Least Squares-Discriminant Analysis (PLS-DA), Classification and Regression Trees (CART), and Cluster Significance Analysis (CSA), specifically proposed for asymmetric classification in QSAR. 

A problem with the classification method is that it provides incentive for incumbents to aggrandize a job title to get it into a higher classification. This may seem appropriate to a manager whose immediate concern is to secure a pay raise for a subordinate but others may see it as underhanded, and it may even lead to a pay discrimination lawsuit. 

The classification methods illustrated in the previous subsection are only a part, although relevant, of the methods proposed in the literature for discriminant classification. Indeed, to cope with the different degrees of complexity that real-world classification problems involve (various degrees of class separability, requiring a corresponding level of nonlinearity in the model statistical assumption which may not always hold insufficient number of observations to estimate the model parameters and so on). As a complete description of all the discriminant techniques goes beyond the scope of the present text, the reader is referred to specific literature covering these other methods in more detail [39-42]. 

This classification problem can then be solved better by developing more suitable boundaries. For instance, using so-called quadratic discriminant analysis (QDA) (Section 33.2.3) or density methods (Section 33.2.5) leads to the boundaries of Fig. 33.2 and Fig. 33.3, respectively [3,4]. Other procedures that develop irregular boundaries are the nearest neighbour methods (Section 33.2.4) and neural nets (Section 33.2.9). 

In Section 18.4, we explained that inductive expert systems can be applied for classification purposes and we refer to that section for further information and example references. It should be pointed out that the method is essentially univariate. Indeed, one selects a splitting point on one of the variables, such that it achieves the best discrimination, the best being determined by, e.g., an entropy function. Several references are given in Chapter 18. A comparison with other methods can be found, for instance, in an article by Mulholland et al. [22]. 

The process of classification in terms of each method of discrimination among diagnostic entities rests on two assumptions. First, the diagnostic entity or subtype is presumed to be a mental disorder. Second, the diagnostic entity is presumed to be discriminable from other mental disorders on some basis. Evaluation of this first assumption returns us to the earlier discussion of what constitutes a mental illness, so we do not need to consider this further. The second assumption raises a new question relevant to classification. Is this condition significantly unique from all other diagnostic categories An answer to this question should be empirically based, but the type of answer received may depend on the methods used to obtain the answer. Next, we consider different methods of classification. 

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). 

Two methods are used to evaluate the predictive ability for LDA and for all other classification techniques. One method consists of dividing the objects of the whole data set into two subsets, the training and the prediction or evaluation set. The objects of the training set are used to obtain the covariance matrix and the discriminant scores. Then, the objects of the training set are classified, so obtaining the apparent error rate and the classification ability, and the objects of the evaluation set are classified to obtain the actual error rate and the predictive ability. The subdivision into the training and prediction sets can be randomly repeated many times, and with different percentages of the objects in the two sets, to obtain a better estimate of the predictive ability. 

Figure 8.1 Schematic classification of complexation measurement methods as a function of the perturbations that they can create at the discriminator (sensitive part of the analytical system that enables differentiation of the chemical species of interest from the other components present) and in solution. The compound reacting with the discriminator and the nature of the discriminator are shown in parentheses, a Constant cell volume methods are less perturbing than variable volumes, b Possibility of ligand release by organisms, c Possibility of interactions with the indicator (ligand with suitable absorbance or fluorescence properties added into the test solution in spectro-metric methods), d Possibility of contamination of very dilute media by ISE membranes (redrawn from Buffle, 1988).

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