Incremental Hyperplane-based Fuzzy Clustering for System Modeling

In this paper, a new incremental hyperplane-based fuzzy clustering method to design a Takagi-Sugeno-Kang (TSK) fuzzy model is proposed. Starting from no rule, it generates clusters based on input similarity and distance from the consequent hyperplane incrementally. Membership functions (MFs) are defined with statistical means and deviations of partitioned data. With this configuration, the obtained clusters reflect the real distribution of the training data properly. The training equations are changed to recursive forms in order to be applied in incremental framework. Some heuristic techniques to guarantee the initial training of each local submodel is used. In order to reduce the dependency on the order of training data, merge step is performed. Merge step is not only important for keeping rule bases compact and interpretable, but also provides the robustness to noise. Some simulations are done to show the advantages and performance of the proposed method.