Norm-Based Localized Generalization Error Model and its Derivation for Radial Basis Function Neural Networks

In pattern classification problems, the generalization error is often defined as the integral of a square function for the entire input space. In this paper, a new localized generalization error model is proposed for radial basis neural networks, which computes the generalization error within a neighborhood of the training samples based on a given norm. Compared with the traditional Mean Square Error term, it is constructed in a more universal perspective way and becomes simpler in calculation for multiple classification problems. Furthermore, the derivation formula of applying this model for Radial basis function neural network is obtained by using stochastic sensitivity measure.