Minimizing Structural Risk on Decision Tree Classification

Tree induction algorithms use heuristic information to obtain decision tree classification. However, there has been little research on how many rules are appropriate for a given set of data, that is, how we can find the best structure leading to desirable generalization performance. In this chapter, an evolutionary multi-objective optimization approach with genetic programming will be applied to the data classification problem in order to find the minimum error rate or the best pattern classifier for each size of decision trees. As a result, we can evaluate the classification performance under various structural complexity of decision trees. Following structural risk minimization suggested by Vapnik, we can determine a desirable number of rules with the best generalization performance. The suggested method is compared with C4.5 application for machine learning data.