For efficient decoding of brain activities in analyzing brain function with an application to brain machine interfacing (BMI), we address a problem of how to determine spatial weights (spatial patterns), bandpass filters (frequency patterns), and time windows (time patterns) by utilizing electroencephalogram (EEG) recordings. To find these parameters, we develop a data-driven criterion that is a natural extension of the so-called common spatial patterns (CSP) that are known to be effective features in BMI. We show that the proposed criterion can be optimized by an alternating procedure to achieve fast convergence. Experiments demonstrate that the proposed method can effectively extract discriminative features for a motor imagery-based BMI. 1. Introduction Brain machine computer interfacing (BMI BCI) is a challenging technology of signal processing, machine learning, and neuroscience [1]. BMIs capture brain activities associated with mental tasks and external stimuli, realize nonmuscular communication, and control channel for conveying messages and commands to the external world [1–3]. Basically, noninvasively measured data such as electroencephalogram (EEG), magnetoencephalogram (MEG), and functional magnetic resonance imaging (fMRI) are widely used to observe brain activities. Among them, because of its simplicity and low cost, EEG is practical for use in engineering applications [4, 5]. Efficient decoding around motor-cortex is a crucial technique for the realization of BMI associated with motor-imagery (MI-BMI) [6, 7] with the application to controlling external devices [7], prostheses [4], rehabilitation [8], and so forth. For instance, it is also known that the real and imaginary movements of hands and feet evoke the change of the so-called mu rhythm in different brain regions [2, 3]. Therefore, the accurate extraction of these changes from the measured EEG signals in the presence of measurement noise and spontaneous components which are related to other brain activities enables us to classify the EEG signal associated with the different motor (imagined) actions such as movement of the right hand, left hand, or feet. In classification of EEG signals in MI-BMI and analyzing of the brain activities during motor imagery, signal processing techniques such as bandpass filtering and spatial weighting are used [1]. For the processing, presuming the parameters such as coefficients of the filters and weights that extract the related components is a crucial issue. Moreover, the optimum parameters in classification are highly dependent on users and
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