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Estimating whole brain dynamics using spectral clustering

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Spectral clustering is a computationally feasible and model-free method widely used in the identification of communities in networks. In this work, we introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. NCPD consists of three parts: spectral clustering allows us to consider high dimensional time series where the dimension of the time series is greater than the number of time points (N > T); the principal angles allows for estimation of the change in terms of network/graph structures across time without prior knowledge of the number or location of the change points; permutation and bootstrapping methods are used to perform inference on the change points. NCPD is applied to various simulated data sets as well as to a resting state functional Magnetic Resonance Imaging (fMRI) data set. The results illustrate the ability of NCPD to observe how the network structure changes over the time course. The new methodology also allows us to identify common functional states across subjects. Finally, the method promises to offer a deep insight into the large-scale characterisations and dynamics of the brain.

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