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2.1 Decision Regions and Functions 27

Figure 2.6. Example of absolute separation of three classes in a two-dimensional
space.

Figure 2.6 also shows Linear decision "surfaces". The decision regions (shaded
areas) are defined as:

Absolute separation lends itself to a hierarchical classification approach as
shown in Figure 2.7. At each level of the hierarchical tree a decision is made
regarding the discrimination of a disjointed group of classes. Each feature vector
(right side of Figure 2.7) is accordingly passed through a decision function. For the
y vs. y discrimination we may use d2,(x) = 4x) - di(x).

Figure 2.7. Hierarchical classification of a feature vector into one of the classes
exemplified in Figure 2.6.

In this example a dichotomic tree, also known as a binary tree, is illustrated.
Although this is a popular type of hierarchical tree, other types of multi-group
discrimination at each level can of course be considered.