Function approximation using LVQ and fuzzy sets

Neural networks with local activation functions, for example RBFNs (Radial Basis Function Networks), 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 to each of which a local activation function is assigned. In RBFNs, this is equivalent to determination of the locations and the numbers of its RBFs, which is generally done based on the distribution of input data. But, in function approximation, the output information (the value of the function to be approximated) must be considered in determination of the local regions. 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. The ordinary LVQ, however, outputs discrete values only, and therefore can not approximate continuous functions. In this paper, fuzzy sets are employed in both of learning and output calculation. Finally, the proposed method uses the back-propagation algorithm for fine adjustment. An example is provided to show the effectiveness of the proposed method.