Using incremental learning algorithms in the search for minimal and effective fuzzy models

The approximation of nonlinear mappings by means of a smooth co-operation (by Gaussian mixture) of several linear experts has become a very popular approach in the connectionist, fuzzy and statistical communities. Two simultaneous types of tuning are required: one concerns the number of the local models whereas the other concerns the fine adjustment of the Gaussian zones and of the local linear models. The goal of this paper is first to compare an incremental and a brute-force algorithm in order to build a minimal and effective fuzzy model for regression problems and then to argue for the advantages gained by using the incremental approach. The two algorithms have been tested on the same benchmark, namely the prediction of Mackey-Glass chaotic time series. We conjecture that fuzzy model architectures, when automatically learned at the structural and parametric level, present a huge number of local minima and that the use of incremental approach can help to travel in a more efficient way in this highly rugged search space