A tunable approximately piecewise linear model derived from the modified probabilistic neural network

A simple model, which can be adjusted by a single smoothing parameter continuously from the best piecewise linear model in each linear subregion to the best approximately piecewise linear model overall, is developed for multivariate general nonlinear regression. The model provides an accurate, smooth, approximately piecewise linear model to cover the entire data space. It provides a logical basis for extrapolation to regions not represented by training data, based on the closest piecewise linear model. This model has been developed by making relatively minor changes to the form of a modified probabilistic neural network (MPNN), which is a network that id used for general nonlinear regression. The MPNN structure allows it to model data by weighting piecewise linear models associated with each of the network´s radial basis functions in the data space