A fast approach to building rough data model through G-K fuzzy clustering

A new method to fast build the rough data model (RDM) by means of fuzzy clustering is proposed. The scheme is contrived by Gustafson-Kessel (GK) algorithm, which is of many good properties and is demonstrated in the data-mining context. In this paper, first we investigate how to integrate the RDM´s classification quality performance index into the GK clustering algorithm in the product space of input and output variables. Then we suggest the way to convert the fuzzy cluster models to rough data models. Hence, we work out an efficient algorithm that can obtain RDMs by just iteratively computing two necessary condition equations, which can minimize the objective function, and turn the multi-dimensional search process of Kowalczyk´s method to one dimensional search strategy (in terms of the number of clusters). This technique reduces the searching time greatly. Moreover, by introducing the concept of the fuzzy degree of fulfillment (DoF) to a cluster rule, our approach seems to be much more flexible and more powerful ability in handling data contaminated by noise, with better generalization ability compared with the traditional rough set theory and the Kowalczyk´s method. Finally, two examples illustrate the effectiveness of our approach.