Fractional Order Modeling of Brain Signals
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Time series modeling and analysis provides means of predicting the future and has been widely used in a variety of fields ranging from seismology for predicting earthquake and volcanic eruption, to finance for risk assessment, and to quantum information processing. The conventional integer order models can only capture short-range dependence; for example, Poisson processes, Markov processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. In time series analysis, one of the conventional assumptions is that the coupling between values at different time instants decreases rapidly as the time difference or distance increases. However, there are situations where strong coupling between values at different times exhibit properties of long range dependence which cannot be processed by the conventional time series analysis. Typical examples of long range dependence signals include financial time series, underwater noise, electroencephalography (EEG) signal, etc. ARFIMA, a fractional order signal processing technique, is the generalization of the conventional integer order techniques, namely, ARIMA and ARMA methods. Hence, it is capable of capturing both short-range dependence and long-range dependence in signals. Compared to conventional integer order models, the ARFIMA model gives a better fit and result when dealing with the data which possess the long range dependence property. In this paper, we investigate the application of the ARFIMA as well as AR methods to model EEG signals obtained from different brain channels. We analyze the resulting correlations for comparison the benefits of ARFIMA over AR on the EEG data exhibiting the long range dependency property. The results showed that the prediction results have a better performance compared to the conventional ARMA models.
KeywordsBrain signals Neurocognitive modeling Fractional order systems Autoregressive Moving Average (ARMA) Electroencephalography (EEG)
The data used in this paper is from a Kaggle competition. This Kaggle competition was sponsored by MathWorks, the National Institutes of Health (NINDS), the American Epilepsy Society and the University of Melbourne, and organized in partnership with the Alliance for Epilepsy Research, the University of Pennsylvania and the Mayo Clinic.
- 1.Loverro, A.: Fractional calculus: history, definitions and applications for the engineer. Report (2004)
- 2.Ilow, J., Leung, H.: Self-similar texture modeling using FARIMA processes with applications to satellite images. IEEE Trans. Image Proces. (2001)
- 3.Geurts, M., Box, G.E.P., Jenkins, G.M.: Time series analysis: forecasting and control. J. Market. Res. (1977)
- 4.Koutsoyiannis, D.: Coupling stochastic models of different timescales. Water Resour. Res. (2001)
- 5.Box, G.E., Jenkins, G.M., Reinsel, G.C.: Time Series Analysis: Forecasting and Control, 4th edn. (2013)
- 6.Barlow, J.S.: Autocorrelation and cross correlation analysis in electroencephalography. IRE Trans. Med. Electron. (1959)
- 7.Hu, J., Zheng, Y., Gao, J.: Long-range temporal correlations, multifractality, and the causal relation between neural inputs and movements. Frontiers Neurol. (2013)
- 8.Palmini, A.: The concept of the epileptogenic zone: a modern look at Penfield and Jasper’s views on the role of interictal spikes. In: Epileptic Disorders (2006)
- 9.Hosking, J.R.: Fractional differencing. Biometrika (1981)