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4.6 Tree Classifiers 135

that the distributions are roughly symmetric although with some deviations in the
covariance matrices, the optimal error achieved with linear discriminants should be
close to what is shown in the classification matrix. The degraded performance
compared with the decision tree approach is evident.
On the other hand, if our only interest is to discriminate class car from all other
ones, a linear classifier with only one feature can achieve this discrimination with a
performance of about 86% (see Exercise 4.8), a comparable result to the one
previously obtained with the tree classififer.

Rules

Figure 4.43. Decision table corresponding to the decision tree shown in Figure
4.41. The "Y", "Nu in the rules columns correspond to the "Yes", "No" branches
followed in the tree.

A formalism often used to represent decision trees is that of decision tables. A
decision table has the layout shown in Figure 4.43 for the breast tissue hierarchical
classification . The three main sectors of the table are:

- The "conditions" rows, corresponding to the decision functions or to any other
type of condition (e.g. categorical conditions such as "colour = red").
- The "actions" rows, corresponding to classifications or to any other type of
actions (e.g. "sound alarm" or "go to Exceptions").
- The "rules" columns, corresponding to the path followed in the decision tree.

The formalism of decision tables is especially suitable when designing a PR
application that needs to incorporate previous expertise from the area where it will
be applied. It provides, then, an easy formalism for the PR designer and the domain
expert to interact. A good example is the design of diagnostic systems in the
medical field.