Application of chaotic noise reduction techniques to chaotic data trained by ANN

We propose a novel method of combining artificial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can significantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be significantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.