Linguistic Rule Extraction from Numerical Data for High-dimensional Classification Problems
Hisao Ishibuchi*, Tadahiko Murata** and Tomoharu Nakashima*
*Department of Industrial Engineering, Osaka Prefecture University Sakai, Osaka 599-8531, Japan
**Department of Industrial and Information Systems Engineering, Ashikaga Institute of Technology Ashikaga, Tochigi 326-8558, Japan
We discuss the linguistic rule extraction from numerical data for high-dimensional classification problems. Difficulties in the handling of high-dimensional problems stem from the curse of dimensionality: the number of combinations of antecedent linguistic values exponentially increases as the number of attributes increases. Our goal is to extract a small number of simple linguistic rules with high classification ability. In this paper, the rule extraction is to find a set of linguistic rules using three criteria: its classification ability, its compactness, and the simplicity of each rule. Our approach consists of two phases: candidate rule generation and rule selection. We first propose a pre-screening method for generating a tractable number of promising candidate rules for high-dimensional classification problems where it is impossible to examine all combinations of antecedent linguistic values. Next we show how genetic algorithms can be applied to the rule selection. Then we combine a heuristic rule elimination procedure with genetic algorithms for improving their search ability. Finally, the performance of our approach is examined by computer simulations on commonly used data sets.