Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatio-temporal decompositions of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatio-temporal patterns and the dynamics of source amplitude across trials; on two brain-computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data.
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