Data Mining: Practical Machine Learning Tools and Techniques, Second Edition

ically, the exception-based rules can very simply be rewritten in terms of regular

if...then...elseclauses. What is gained by the formulation in terms of excep-

tions is not logicalbut psychological.We assume that the defaults and the tests

that occur early apply more widely than the exceptions further down. If this is

indeed true for the domain, and the user can see that it is plausible, the expres-

sion in terms of (common) rules and (rare) exceptions will be easier to grasp

than a different, but logically equivalent, structure.

3.6 Rules involving relations

We have assumed implicitly that the conditions in rules involve testing an

attribute value against a constant. Such rules are called propositionalbecause the

attribute-value language used to define them has the same power as what logi-

cians call the propositional calculus.In many classification tasks, propositional

rules are sufficiently expressive for concise, accurate concept descriptions. The

weather, contact lens recommendation, iris type, and acceptability of labor con-

tract datasets mentioned previously, for example, are well described by propo-

sitional rules. However, there are situations in which a more expressive form of

rule would provide a more intuitive and concise concept description, and these

are situations that involve relationships between examples such as those encoun-

tered in Section 2.2.

Suppose, to take a concrete example, we have the set of eight building blocks

of the various shapes and sizes illustrated in Figure 3.6, and we wish to learn

the concept ofstanding.This is a classic two-class problem with classes stand-

ingand lying. The four shaded blocks are positive (standing)examples of the

concept, and the unshaded blocks are negative (lying)examples. The only infor-

3.6 RULES INVOLVING RELATIONS 73

Shaded:

Unshaded:

standing

lying

Figure 3.6The shapes problem.