A Study of the Influence of Rule Measures in Classifiers Induced by Evolutionary Algorithms

The Pittsburgh representation is a well-known encoding for symbolic classifiers in evolutionary algorithms, where each individual represents one symbolic classifier, and each symbolic classifier is composed by a rule set. These rule sets can be interpreted as ordered or unordered sets. The major difference between these two approaches is whether rule ordering defines a rule precedence relationship or not. Although ordered rule sets are simple to implement in a computer system, the rule set is difficult to be interpreted by human domain experts, since rules are not independent from each other. In contrast, unordered rule sets are more flexible regarding their interpretation. Rules are independent from each other and can be individually presented to a human domain expert. However, the algorithm to decide a classification of a given example is more complex. As rules have no precedence, an example should be presented to all rules at once and some criteria should be established to decide the final classification based on all fired rules. A simple approach to decide which rule should provide the final classification is to select the rule that has the best rating according to a chosen quality measure. Dozens of measures were proposed in literature; however, it is not clear whether any of them would provide a better classification performance. This work performs a comparative study of rule performance measures for unordered symbolic classifiers induced by evolutionary algorithms. We compare 9 rule quality measures in 10 data sets. Our experiments point out that confidence (also known as precision) presented the best mean results, although most of the rule quality measures presented approximated classification performance assessed with the area under the ROC curve (AUC).