International Journal of Bifurcation and Chaos, Vol. 25, No. 14 (2015) 1540023 (9 pages) c  World Scientific Publishing Company DOI: 10.1142/S0218127415400234 Testing the Self-Similarity Exponent to Feature Extraction in Motor Imagery Based Brain Computer Interface Systems Germ´anRodr´ ıguez-Berm´ udez University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain german.rodriguez@cud.upct.es Miguel ´ Angel S´ anchez-Granero Department of Mathematics, Universidad de Almer´ ıa, 04120 Almer´ ıa, Spain Pedro J. Garc´ ıa-Laencina, Manuel Fern´ andez-Mart´ ınez, Jos´ e Serna and Joaqu´ ın Roca-Dorda University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain Received December 15, 2014; Revised July 1, 2015 A Brain Computer Interface (BCI) system is a tool not requiring any muscle action to transmit information. Acquisition, preprocessing, feature extraction (FE), and classification of electroen- cephalograph (EEG) signals constitute the main steps of a motor imagery BCI. Among them, FE becomes crucial for BCI, since the underlying EEG knowledge must be properly extracted into a feature vector. Linear approaches have been widely applied to FE in BCI, whereas nonlin- ear tools are not so common in literature. Thus, the main goal of this paper is to check whether some Hurst exponent and fractal dimension based estimators become valid indicators to FE in motor imagery BCI. The final results obtained were not optimal as expected, which may be due to the fact that the nature of the analyzed EEG signals in these motor imagery tasks were not self-similar enough. Keywords : Brain computer interface; Hurst exponent; fractal dimension; generalized Hurst exponent; feature extraction; Fisher linear discriminant. 1. Introduction In 1929, Hans Berger published the first known study for human EEG signals [Berger, 1929]. Since then, EEG signals have been intensively studied and nowadays they are successfully used in a great vari- ety of both medical and nonmedical applications [Sanei & Chambers, 2008]. Further, in the last years, the advances in EEG signal processing techniques as well as in electronic equipment have made easier the development of BCI systems [Bashashati et al., 2007]. The main purpose of a BCI system is to pro- vide a new way to communicate without requir- ing any muscle action. Overall, a BCI system for Motor Imagery (MI) paradigm follows the general scheme shown in Fig. 1. Indeed, at a first stage, EEG signals are measured using electrodes placed on the scalp at some locations. Note that the num- ber of required electrodes depends on each specific application (usually, from 2 to 128 positions). Sub- sequently, EEG signals are preprocessed in order to eliminate noise and artifacts. Later, BCI system 1540023-1 Int. J. Bifurcation Chaos 2015.25. Downloaded from www.worldscientific.com by CITY UNIVERSITY OF HONG KONG on 01/16/16. For personal use only.