Analysis of augmented-input-Layer RBFNN

In this paper we present and analyze a new structure for designing a radial basis function neural network (RBFNN). In the training phase, input layer of RBFNN is augmented with desired output vector. Generalization phase involves the following steps: 1) identify the cluster to which a previously unseen input vector belongs; 2) augment the input layer with an average of the targets of the input vectors in the identified cluster; and 3) use the augmented network to estimate the unknown target. It is shown that, under some reasonable assumptions, the generalization error function admits an upper bound in terms of the quantization errors minimized when determining the centers of the proposed method over the training set and the difference between training samples and generalization samples in a deterministic setting. When the difference between the training and generalization samples goes to zero, the upper bound can be made arbitrarily small by increasing the number of hidden neurons. Computer simulations verified the effectiveness of the proposed method.