Adaptive tree-structured self-generating radial basis function network and its performance evaluation

AbstractSeveral algorithms have been proposed to identify a large scale system, such as the neuro-fuzzy GMDH, and the fuzzy modeling using a fuzzy neural network, As another approach, Sanger proposed a tree-structured adaptive network. But in Sanger's network, it is not clear how to determine the initial disposition of bases and the number of bases in each subtree. We propose a nonlinear modeling method called the adaptive tree-structured self-generating radial basis function network (ATree0RBFN). In ATree-RBFN, we take the maximum absolute error (MAE) selection method in order to improve Sanger's model. We combine Sanger's tree-structured adaptive network for an overall model structure with the MAE selection method for a subtree identification problem. In ATree-RBFN, the tuning parameters are not only the coefficients but also the centers and widths of bases, and a subtree can be generated under all leaf nodes. Then, the input-outpu data can be divided into the training data set and the checking data set, and an element of inputs in each subtree is selected according to the corresponding error value from the checking data set. We also demonstrate the effectiveness of the proposed method by solving several numerical examples