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In this paper, we propose LGG, a neurologically inspired graph neural network, to learn local-global-graph representations from Electroencephalography (EEG) for a Brain-Computer Interface (BCI). A temporal convolutional layer with multi-scale 1D convolutional kernels and kernel-level attention fusion is proposed to learn the temporal dynamics of EEG. Inspired by neurological knowledge of cognitive processes in the brain, we propose local and global graph-filtering layers to learn the brain activities within and between different functional areas of the brain to model the complex relations among them during the cognitive processes. Under the robust nested cross-validation settings, the proposed method is evaluated on the publicly available dataset DEAP, and the classification performance is compared with state-of-the-art methods, such as FBFgMDM, FBTSC, Unsupervised learning, DeepConvNet, ShallowConvNet, EEGNet, and TSception. The results show that the proposed method outperforms all these state-of-the-art methods, and the improvements are statistically significant (p<0.05) in most cases. The source code can be found at: https://github.com/yi-ding-cs/LGG
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