Multilayer perceptron based optimal state space reconstruction for time series modelling

Estimating the nonlinear dynamical system which has generated a given time series is considered. Traditionally, this is achieved via two separate steps: projecting the signal frames onto the state space, and then estimating the predictive relationship between successive state vectors. In the method presented here, these two steps are performed simultaneously, where both the projection and prediction functions are represented by MLPs. In addition, a measurement function, again represented by an MLP, is used. This MLP maps each state vector to a sample of the given signal. Original estimation problem is then interpreted as a training (optimization) problem, and a backpropagation type training algorithm is proposed for solving it. The method proposed is tested with an artificial time series produced by Henon map and a speech signal. Performances are compared with those of popular traditional methods, which indicates the clear superiority of this method