  Functional magnetic resonance imaging (fMRI) time series data presents a
unique opportunity to understand temporal brain connectivity, and models that
uncover the complex dynamic workings of this organ are of keen interest in
neuroscience. Change point models can capture and reflect the dynamic nature of
brain connectivity, however methods that translate well into a high-dimensional
context (where $p>>n$) are scarce. To this end, we introduce
$\textit{factorized binary search}$ (FaBiSearch), a novel change point
detection method in the network structure of multivariate high-dimensional time
series. FaBiSearch uses non-negative matrix factorization, an unsupervised
dimension reduction technique, and a new binary search algorithm to identify
multiple change points. In addition, we propose a new method for network
estimation for data between change points. We show that FaBiSearch outperforms
another state-of-the-art method on simulated data sets and we apply FaBiSearch
to a resting-state and to a task-based fMRI data set. In particular, for the
task-based data set, we explore network dynamics during the reading of Chapter
9 in $\textit{Harry Potter and the Sorcerer's Stone}$ and find that change
points across subjects coincide with key plot twists. Further, we find that the
density of networks was positively related to the frequency of speech between
characters in the story. Finally, we make all the methods discussed available
in the R package $\textbf{fabisearch}$ on CRAN.
