Tree structured non-linear signal modeling and prediction

We develop a non-parametric method of nonlinear prediction based on adaptive partitioning of the phase space associated with the process. The partitioning method is implemented with a recursive tree-structured vector quantization algorithm which successively refines the partition by binary splitting where the splitting threshold is determined by a penalized maximum entropy criterion. A complexity penalty is derived and applied to protect against high statistical variability of the predictor structure. We establish an important relation between our tree-structured model for the process and generalized non-linear thresholded AR model (ART). We illustrate our method for two cases where classical linear prediction is ineffective: a chaotic "double-scroll" signal measured at the output of a Chua-type electronic circuit, and a simulated second order ART model.