Identifying Local Ultrametricity of EEG Time Series for Feature Extraction in a Brain-Computer Interface

The accurate discrimination of EEG times-series is a challenging problem and has become a topic of prominent research interest, given the extent of the research activity in the area of brain-computer interface (BCI) technology. Many signal processing algorithms involving preprocessing, feature extraction/selection, and classification have been deployed and yet, the most appropriate and robust solutions are still being sought. This paper presents an analysis of a new methodology for feature extraction in a BCI which is based on identifying the extent of ultrametricity from EEG time-series. This work is inspired by the idea that there are natural, not necessarily unique, tree or hierarchy structures defined by the ultrametric topology of EEG time-series. The objective is to determine if coefficients which reflect the extent of ultrametricity can be used as distinct features of different EEG time series, recorded whilst subjects imagine left/right hand movements (motor imagery(MI)). The results show that MI based EEG time-series can be separated using a local ultrametricity quantifier and a linear discriminant classifier or Bayes classifier. Also, it is shown that neural-time-series-prediction-preprocessing (NTSPP) produces a higher dimensional space in which local ultrametricity is more separable for two classes of EEG signals.