Function approximation using LVQ and fuzzy sets

Neural networks with local activation functions have a merit of excellent generalization abilities. When this type of network is used in function approximation, it is very important to determine the proper division of the input space into local regions where each of which a local activation function is assigned. A new method is proposed that uses LVQ network to approximate the functions based on the output information. It divides the input space into regions with a prototype vector at the center of each region. However, an ordinary LVQ outputs discrete values only, and therefore can not approximate continuous functions. In this paper, fuzzy sets are employed in both learning and output calculation. Finally, the proposed method uses the backpropagation algorithm for fine adjustment. An example is provided to show the effectiveness of the proposed method