Discriminative Metric Learning on Extended Grassmann Manifold for Classification of Brain Signals

Electroencephalography (EEG) and magnetoencephalography (MEG) measure the brain signal from spatially-distributed electrodes. In order to detect event-related synchronization and desynchronization (ERS/ERD), which are utilized for brain-computer/machine interfaces (BCI/BMI), spatial filtering techniques are often used. Common spatial potential (CSP) filtering and its extensions which are the spatial filtering methods have been widely used for BCIs. CSP transforms brain signals that have a spatial and temporal index into vectors via a covariance representation. However, the variance-covariance structure is essentially different from the vector space, and not all the information can be transformed into an element of the vector structure. Grassmannian embedding methods, therefore, have been proposed to utilize the variance-covariance structure of variational patterns. In this paper, we propose a metric learning method to classify the brain signal utilizing the covariance structure. We embed the brain signal in the extended Grassmann manifold, and classify it on the manifold using the proposed metric. Due to this embedding, the pattern structure is fully utilized for the classification. We conducted an experiment using an open benchmark dataset and found that the proposed method exhibited a better performance than CSP and its extensions.