Exploiting Neurons with Localized Receptive Fields to Learn Chaos
K. Stokbro
D. K. Umberger
J. A. Hertz
The Niels Bohr Institute,
Blegdamsvej 17, DK-2100 Copenhagen O, Denmark
Abstract
We propose a method for predicting chaotic time series that can be viewed either as a weighted superposition of linear maps or as a neural network whose hidden units have localized receptive fields. These receptive fields are constructed from the training data by a binary-tree algorithm. The training of the hidden-to-output weights is fast because of the localization of the receptive fields. Numerical experiments indicate that for a fixed number of free parameters, this weighted-linear-map scheme is superior to its constant-map counterpart studied by Moody and Darken. We also find that when the amount of data available is limited, this method outperforms the local linear predictor of Farmer and Sidorowich.
