Automatic generation of RBF networks using wavelets

Learning can be viewed as mapping from an input space to an output space. Examples of these mappings are used to construct a continuous function that approximates the given data and generalizes for intermediate instances. Radial-basis function (RBF) networks are used to formulate this approximating function. A novel method is introduced that automatically constructs a generalized radial-basis function (GRBF) network for a given mapping and error bound. This network is shown to be the smallest network within the error bound for the given mapping. The integral wavelet transform is used to determine the parameters of the network. Simple one-dimensional examples are used to demonstrate how the network constructed using the transform is superior to that constructed using standard ad hoc optimization techniques. The paper concludes with the automatic generation of GRBF networks for a multi-dimensional problem, namely, real-time 3D object recognition and pose estimation. The results of this application are favorable.