Types of classification rules

There are many types of pattern recognition which essentially differ in the way they define classification rules. In this section, we will describe some of the approaches, which we will then develop further in the following sections. We will not try to develop a classification of pattern recognition methods but merely indicate some characteristics of the methods, that are found most often in the chemometric literature and some differences between those methods. 

A first distinction which is often made is that between methods focusing on discrimination and those that are directed towards modelling classes. Most methods explicitly or implicitly try to find a boundary between classes. Some methods such as linear discriminant analysis (LDA, Sections 33.2.2 and 33.2.3) are designed to find explicit boundaries between classes while the k-nearest neighbours (A -NN, Section 33.2.4) method does this implicitly. Methods such as SIMCA (Section 33.2.7) put the emphasis more on similarity within a class than on discrimination between classes. Such methods are sometimes called disjoint class modelling methods. While the discrimination oriented methods build models based on all the classes concerned in the discrimination, the disjoint class modelling methods model each class separately. 

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). 

One of the problems with discrimination-oriented methods is that we need to classify each object in one of the given classes. It is, however, quite possible that an 

The conceptually simplest model, which for reasons explained later is called UNEQ, is based on the multivariate normal distribution. Suppose we have carried 

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