Estimating noise and dimensionality in BCI data sets: Towards BCI illiteracy comprehension

About one third of the BCI subjects cannot communicate via BCI, a phenomenon that is known as BCI illiteracy. New investigations aiming to an early prediction of illiteracy would be very helpful to understand this phenomenon and to avoid hard BCI training for many subjects. In this paper, the first application on to electroencephalogram (EEG) of a newly developed machine learning tool, Relevant Dimension Estimation (RDE), is presented. RDE is capable to estimate the intrinsic noise present in a data set and the dimensionality of the learning problem, extracting from the data the label relevant information. Applied to EEG data collected during motor imagery paradigms in many BCI sessions, RDE is able to deliver interesting insight into the illiteracy phenomenon. In particular, RDE can demonstrate that illiteracy is mostly not due to the non-stationarity or high dimensionality present in the data, but rather due to a high intrinsic noise in the label related information. Moreover, RDE allows to detect individual BCI-illiterate subjects from a small amount of example data in a very reliable way, based on a combination of the estimated noise, the dimensionality and the width of the chosen kernel.