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

the first test in the rule, split the space vertically as shown in the center picture.

This gives the beginnings of a rule:

If x >1.2 then class =a

However, the rule covers many b’s as well as a’s, so a new test is added to the

rule by further splitting the space horizontally as shown in the third diagram:

If x >1.2 and y >2.6 then class =a

This gives a rule covering all but one of the a’s. It’s probably appropriate to leave

it at that, but if it were felt necessary to cover the final a,another rule would be

necessary—perhaps

If x >1.4 and y <2.4 then class =a

The same procedure leads to two rules covering the b’s:

If x £1.2 then class =b

If x >1.2 and y £2.6 then class =b

106 CHAPTER 4| ALGORITHMS: THE BASIC METHODS

Figure 4.6Covering algorithm: (a) covering the instances and (b) the decision tree for

the same problem.

x > 1.2?

b

no

y > 2.6?

yes

b

no

a

yes

(b)