Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matrices
This work addresses the challenge of statistically analyzing dynamic brain connectivity for neuroscience researchers, offering an incremental improvement with a novel dimensionality reduction technique.
The paper tackles the problem of analyzing dynamic brain functional connectivity by representing time-series data as trajectories on the space of covariance matrices, using a metric-based approach for clustering and classification, and achieves task classification rates that match or outperform state-of-the-art techniques on Human Connectome Project data.
Human brain functional connectivity (FC) is often measured as the similarity of functional MRI responses across brain regions when a brain is either resting or performing a task. This paper aims to statistically analyze the dynamic nature of FC by representing the collective time-series data, over a set of brain regions, as a trajectory on the space of covariance matrices, or symmetric-positive definite matrices (SPDMs). We use a recently developed metric on the space of SPDMs for quantifying differences across FC observations, and for clustering and classification of FC trajectories. To facilitate large scale and high-dimensional data analysis, we propose a novel, metric-based dimensionality reduction technique to reduce data from large SPDMs to small SPDMs. We illustrate this comprehensive framework using data from the Human Connectome Project (HCP) database for multiple subjects and tasks, with task classification rates that match or outperform state-of-the-art techniques.