Name
Abstract | ||
|---|---|---|
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 |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1109/78.796437 | IEEE Trans. Signal Processing |
Keywords | Field | DocType |
Predictive models,Signal processing,State-space methods,Subspace constraints,Regression tree analysis,Impurities,Mean square error methods,Chaos,Electronic circuits,Nearest neighbor searches | k-nearest neighbors algorithm,Singular value decomposition,Mathematical optimization,Nonlinear system,Minimum mean square error,Mean squared error,Linear prediction,State space,Mathematics,Piecewise | Journal |
Volume | Issue | ISSN |
47 | 11 | 1053-587X |
Citations | PageRank | References |
15 | 0.82 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olivier J. j. Michel | 1 | 232 | 23.78 |
| A.O. Hero, III | 2 | 590 | 53.94 |
| Anne-Emmanuelle Badel | 3 | 15 | 0.82 |