Dimensionality Reduction via the Laplace-Beltrami Operator: Application to EEG-based BCI

Abstract

Neural oscillations captured by electroencephalography (EEG) can be used by Brain-Computer Interfaces (BCIs) to reveal the underlying mental processes and enable explicitly or implicitly interacting with one s environment. Most feature extraction techniques are based on spatial filters and power analyses in multiple frequency bands. The global geometry feature is seldom investigated. In this paper, the spatial aspects of EEG signals are studied using the Laplace-Beltrami operator. The eigenvectors of the Laplace-Beltrami operator form an orthonormal basis for square-integrable functions over the scalp and capture the geometry of electrodes position in a hierarchical way. The signals are decomposed into different spatial frequency components by the projection into the eigenspaces of the Laplace-Beltrami operator. Dimensionality reduction could be done by using only the low frequency components. This method is compared with Principal Component Analysis (PCA) filtering on publicly available motor imagery BCI data and achieved comparable results while being unsupervised, data-independent and requiring 33.7% less computation time.