Artificial Neural Network Architecture Design for EEG Time Series Simulation Using Chaotic System

Abstract

This paper investigates the training performances of multilayer artificial neural network (ANN) architectures for the generation and prediction of Lorenz chaotic system. Given that the complexity of ANN architectures are at the same level, the training performances of ANN with only one hidden layer prevail over those of ANN with multiple hidden layers. The designed ANN model is used to simulate and analyze brain activities captured by Electroencephalogram (EEG). Previous research shows that EEG signals demonstrate chaotic patterns. Chaotic systems can be represented by a set of mathematical equations. The three differential equations of Lorenz chaotic system are used to generate the ANN training samples. The ANN training is carried out using MATLAB Neural Network Toolbox with three training algorithms and the Nonlinear autoregressive (NAR) model from the nonlinear time series tool ‘ntstool’. ANN architectures with two hidden layers combined with different number of hidden neurons and input delays are compared by measuring the training performance using the average mean square errors (MSE) of all training samples. The training results demonstrate that the training performance can not be improved simply by increasing the complexity of the ANN architecture in terms of the number of hidden layers and hidden neurons. The simplicity of ANN architecture will further benefit the hardware implementation in the application for the generation and prediction of chaotic systems time series to simulate EEG signals for brain research.