Robust Support Matrix Machine for Single Trial EEG Classification

Electroencephalogram (EEG) signals are of complex structure and can be naturally represented as matrices. Classification is one of the most important steps for EEG signal processing. Newly developed classifiers can handle these matrix-form data by adding low-rank constraint to leverage the correlation within each data. However, classification of EEG signals is still challenging, because EEG signals are always contaminated by measurement artifacts, outliers, and non-standard noise sources. As a result, existing matrix classifiers may suffer from performance degradation, because they typically assume that the input EEG signals are clean. In this paper, to account for intra-sample outliers, we propose a novel classifier called a robust support matrix machine (RSMM), for single trial EEG data in matrix form. Inspired by the fact that empirical EEG signals contain strong correlation information, we assume that each EEG matrix can be decomposed into a latent low-rank clean matrix plus a sparse noise matrix. We simultaneously perform signal recovery and train the classifier based on the clean EEG matrices. We formulate our RSMM in a unified framework and present an effective solver based on the alternating direction method of multipliers. To evaluate the proposed method, we conduct extensive classification experiments on real binary EEG signals. The experimental results show that our method has outperformed the state-of-the-art matrix classifiers. This paper may lead to the development of robust brain-computer interfaces (BCIs) with intuitive motor imagery and thus promote the broad use of the noninvasive BCIs technology.