Evaluation of fractal dimension estimation methods for feature extraction in motor imagery based brain computer interface

A brain computer interface (BCI) enables direct communication between a brain and a computer translating brain activity into computer commands using preprocessing, feature extraction and classification operations. Feature extraction is crucial as it has a substantial effect on the classification accuracy and speed. While fractal dimension has been successfully used in various domains to characterize data exhibiting fractal properties, its usage in motor imagery based BCI has been more recent. There are several fractal dimension estimation methods, some of which are not applicable to all types of data exhibiting fractal properties. In this study, commonly used fractal dimension estimation methods to characterize time series (Katz’s method, Higuchi’s method and the rescaled range method) were evaluated for feature extraction in motor imagery based BCI by conducting offline analyses of a two class motor imagery dataset. Different classifiers (fuzzy k nearest neighbors (FKNN), support vector machine and linear discriminant analysis) were tested in combination with these methods to determine the methodology with the best performance. This methodology was then modified by implementing the time dependent fractal dimension (TDFD), differential fractal dimension and differential signals methods to determine if the results could be further improved. Katz’s method with FKNN resulted in the highest classification accuracy (of 85%), and further improvements (by 3%) were achieved by implementing the TDFD method. The results point to Katz’s method with FKNN as a favorable methodology for motor imagery based BCI and warrant further research to implement this methodology in online analysis of motor imagery data and analysis of other signals.