Factorized Binary Search: change point detection in the network structure of multivariate high-dimensional time series

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.