A Method for Determining Decision Tree Complexities Based on Multiobjective Optimization for Online Learning Community

Abstract

This paper focuses on finding minimal complexities of decision trees representing rules defined for features and functionalities of online learning community. Because simultaneously minimizing all complexities is not always possible and this matches pattern of multiobjective optimization, Pareto optimal point is introduced for describing complexity distributions for selecting decision tree most suitable for system requirements. Unlike typical multiobjective optimization whose feasible space can be explicitly represented, feasible space for complexities of decision trees can only be implicitly reflected by relationships of subtables and associated objective functions due to the great number of possible trees. This paper provides a means of finding Pareto optimal points in implicit feasible space determined by objective functions defined for describing decision tree complexities by using graph and associated algorithm. The experimental results show that proposed algorithm yields valid results for finding Pareto optimal points.