Adaptive radial basis functions

We develop adaptive radial basis functions: kernel-based models for regression and discrimination where the functional form of the basis function depends on the data. The approach may be regarded as a radial form of projection pursuit, with the additional constraint that the basis functions have a common functional form. We develop the approach for regression and extend it to discrimination via optimal scaling. The motivation behind this study is twofold: (1) the requirement for suitable basis functions for high-dimensional data and (2) to assess optimal scaling as an alternative criterion for training nonlinear models. We assess the approach for regression and discrimination using simulated data