Toshinobu Harada

Data fitting with a spline using a real-coded genetic algorithm

To obtain a good approximation for data fitting with a spline, frequently we have to deal with knots as variables. The problem to be solved then becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain the global optimum. In this paper, we propose a method for solving this problem by using a real-coded genetic algorithm. Our method can treat not only data with a smooth underlying function, but also data with an underlying function having discontinuous points and/or cusps. We search for the best model among candidate models by using the Bayes Information Criterion (BIC). With this, we can appropriately determine the number and locations of knots automatically and simultaneously. Five examples of data fitting are given to show the performance of our method.

Decision rule visualization for knowledge discovery by means of rough set approach

Recently, the application studies of rough set theory to real problems have been increasing. The discovery of useful decision rules is a key to a success of the rough set applications. However, finding useful decision rules is often difficult when a lot of decision rules are induced by the rough set approach. In this study, we develop a decision rule visualization system for supporting the discovery of useful decision rules. The system visualizes decision rules having same conclusions in three-dimensional coordinate having the vertical axis of co-occurrence rates between atomic formulae and conclusions and two other axes obtained by Hayashis quantification method IV using co-occurrence rates between atomic formulae as similarities. An experiment is conducted to evaluate the proposed system. The results show that useful decision rules are discovered efficiently from many decision rules. Moreover, we show the usability of the system by numerical experiments using car data.