Exploiting Neurons with Localized Receptive Fields to Learn Chaos

We pr opose a method for predict ing chaotic time series that can be viewed eit her as a weighted superposit ion of linear maps or as a neural network whose hidden units have localized receptive fields. These receptive fields are constructed from the tra ining data by a binary-tree algorithm. The trainin g of the hidden-t o-output weights is fast because of the localization of the receptive fields. Numerical experiments indicat e that for a fixed number of free parameters, this weighted-linear-m ap scheme is superior to its constant-map counterpart studied by Moody and Darken. We also find th at when th e amount of data available is limit ed, thi s method outperforms th e local linear predictor of Farmer and Sidorowich.