Tree-structured nonlinear signal modeling and prediction
Michel, O.J.J.; Hero, A.O., III; Badel, A.E.
Signal Processing, IEEE Transactions on
Volume 47, Issue 11, Nov 1999 Page(s):3027 - 3041
Digital Object Identifier 10.1109/78.796437
Summary:We develop a regression tree approach to identification and
prediction of signals that evolve according to an unknown nonlinear
state space model. In this approach, a tree is recursively constructed
that partitions the p-dimensional state space into a collection of
piecewise homogeneous regions utilizing a 2p-ary splitting
rule with an entropy-based node impurity criterion. On this partition,
the joint density of the state is approximately piecewise constant,
leading to a nonlinear predictor that nearly attains minimum mean square
error. This process decomposition is closely related to a generalized
version of the thresholded AR signal model (ART), which we call
piecewise constant AR (PCAR). We illustrate the 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 second-order ART model. We show that the
prediction errors are comparable with the nearest neighbor approach to
nonlinear prediction but with greatly reduced complexity
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