Identifying Coherent Subgraphs In Dynamic Brain Networks

Dynamic graphs are natural abstractions for modeling correlations in brain activity. These correlation graphs are constructed from time-series signals corresponding to neuronal activity in different regions of the brain over suitably selected time windows, by linking correlated regions via edges. An important problem in the context of these dynamic correlation graphs is the discovery of sets of regions of the brain, whose activity level is temporally coherent. These manifest as temporally persistent sub-graphs that are strongly connected, referred to as \emph{coherent subgraphs}. In this paper, we present a model and method for identifying coherent subgraphs in dynamic correlation graphs. We show that densely connected components in correlation graphs can be effectively modeled as low-rank sub-matrices derived from the time series signals. Specifically, we derive theoretical results showing that quasi cliques in a correlation graph can be inferred from rows of the left singular matrix of its time-series, and can be tracked in time to identify coherent subgraphs. We apply our proposed method to real-world time-series data from functional MRIs. We show that signals corresponding to nodes in coherent subgraphs can accurately predict whether the subject was actively performing a cognitive task, or was at rest. Furthermore, we also show that the same set of nodes can predict task outcomes/ conditions (such as win v/s loss in a gambling task). To the best of our knowledge, our work is the first in theoretically modeling and analyzing dynamic brain networks using spectral decomposition of the windowed time-series.