An adaptive sub-space filter model

Abstract

A tunable approximate piecewise linear regression model [A. Zaknich, Y. Attikiouzel, December 2000] has been previously developed, which can be adjusted by a single smoothing parameter continuously from the best piecewise linear model in each sub-space to the best approximate piecewise linear model over the whole data space. A suitable value in between ensures that all neighbouring piecewise linear models merge together smoothly at their boundaries. This model was developed by making relatively minor changes to the form of the modified probabilistic neural network [A. Zaknich, July 1998], a network used for general nonlinear regression. The special modified probabilistic neural network (MPNN) structure allows it to be easily used to model a process by appropriately weighting piecewise linear models associated with each piecewise linear models associated with each of the network's radial basis functions, which together cover the data space. The model has now bee further extended to allow each piecewise linear model section to be adapted separately as new data flows through it. By doing this, the proposed adaptive sub-space filter (ASF) model represents a learning/filtering method for nonlinear processes that provides a solution to the stability/plasticity dilemma associated with standard adaptive filters.