Chaotic System Design Based on Recurrent Artificial Neural Network for the Simulation of EEG Time Series

Chaotic System Design Based on Recurrent Artificial Neural Network for the Simulation of EEG Time Series

Lei Zhang (University of Regina, Regina, Canada)
DOI: 10.4018/IJCINI.2019010103

Abstract

Electroencephalogram (EEG) signals captured from brain activities demonstrate chaotic features, and can be simulated by nonlinear dynamic time series outputs of chaotic systems. This article presents the research work of chaotic system generator design based on artificial neural network (ANN), for studying the chaotic features of human brain dynamics. The ANN training performances of Nonlinear Auto-Regressive (NAR) model are evaluated for the generation and prediction of chaotic system time series outputs, based on varying the ANN architecture and the precision of the generated training data. The NAR model is trained in open loop form with 1,000 training samples generated using Lorenz system equations and the forward Euler method. The close loop NAR model is used for the generation and prediction of Lorenz chaotic time series outputs. The training results show that better training performance can be achieved by increasing the number of feedback delays and the number of hidden neurons, at the cost of increasing the computational load.
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Background

ANN is a machine learning method. It can be used for pattern recognition and prediction of multi-variant time series. The training performance of an ANN depends on its architecture and the training data. ANN architecture is inspired by biological neural network of the human brain. The classical feedforward ANN architecture includes an input layer, a number of hidden layers and an output layer. Each hidden layer includes a number of parallel distributed hidden neurons. Compared to other machine learning methods, the advantage of ANN design is that an ANN can be trained without knowing the features of the training data beforehand. The disadvantage is that it requires a large number of training data to obtain good ANN training performance. Forecasting using ANN can be dated back to two decades ago (Zhang, 1998) and has been successfully adopted for time series pattern recognition and prediction in many applications. Recent publications have shown promising research advances in optimizing ANN architecture and training algorithm for time series prediction (Zhang, 2018).

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