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2 Pattern Discrimination

2.1 Decision Regions and Functions

We saw in the previous chapter that in classification or regression tasks, patterns
are represented by feature vectors in an 9id feature space. In the particular case of
a classifier. the main goal is to divide the feature space into regions assigned to the
classification classes. These regions are called decision regions. If a feature vector
falls into a certain decision region the associated pattern is assigned to the
corresponding class.
Let us assume two classes u, e 02 of patterns described by two-dimensional
feature vectors (coordinates x, and x2) as shown in Figure 2.1.

Figure 2.1. Two classes of patterns described by two-dimensional feature vectors
(features x, and x2).

Each pattern is represented by a vector x = [x, x,]' E 91'. In Figure 2.1 we
used "0" to denote class u, patterns and "x" to denote class 02 patterns. In general,
the patterns of each class will be characterized by random distributions of the
corresponding feature vectors, as illustrated in Figure 2.1 where the ellipses
represent "boundaries" of the distributions, also called class limits.
Figure 2.1 also shows a straight line separating the two classes. We can easily
write the equation of the straight line in terms of the coordinates (features) x,, x2