M-Estimation-Based Subspace Learning for Brain Computer Interfaces

Many problems in signal processing, statistical learning, and data science can be posed as the problem of learning lower dimensional representation of the data. Particularly, we consider the brain computer interface (BCI) application where electroencephalography (EEG) data are used to determine user's intent to type letters through stimulation with rapid serial visual presentations (RSVP). Such a typing system requires dimensionality reduction and classification abilities. The former is achieved through principal component analysis (PCA), whereas the latter involves regularized discriminant analysis (RDA). Remarkably, EEG recordings are prone to contain user-produced artifacts, such as eye blinks, jaw contractions, or scalp movements. In this article, we present a methodology to fully robustify the aforementioned BCI application, enhancing its suitability in challenging recording scenarios. We consider a solution for robust PCA (RPCA) of fully observed data with outlying samples based on M-estimation theory, as well as a similar methodology for robust RDA (RRDA). Our proposed algorithm iteratively yields robust mean vector and covariance matrix estimates, and then applies eigenanalysis on the estimated robust covariance matrix. The result is a principled way of dealing with outliers in the data that is simple, yet effective in delivering remarkable classification performance. The methodology is validated with real EEG data and compared to the state-of-the-art RSVP Keyboard, with a thorough experimental setup being recorded and described.