Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions.  Goal : The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain.  Method : In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes.  Results : The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with  a priori  known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures.  Conclusion : The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization.  Significance : The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.
['Arash Golibagh Mahyari', 'David M. Zoltowski', 'Edward M. Bernat', 'Selin Aviyente']
A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG