Analysis of Dynamic Brain Connectivity Through Geodesic Clustering

Analysis of dynamic functional connectivity allows for studying the time variant behavior of brain connectivity during specific tasks or at rest. There is, however, a debate around the significance of studies analyzing the dynamic connectivity, as it is usually estimated using short subsequences of the entire time-series. Therefore, a question that naturally arises is whether the dynamic connectivity information is robust enough to compare connectivity matrices. In this paper we investigate the importance of the choice of metric on the space of graphs to answer this question, using a dataset of twins under the assumption that twins connectivity is more similar than in any other pair of unrelated subjects. Specifically, the problem was formulated as a classification task between twin and non-twin pairs. The approach described in the paper relies on geodesic clustering of dynamic connectivity matrices to find a subset of brain states, which were then used to encode the pairwise connectivity similarities between subjects. Experiments were performed to compare the use of Euclidean distance in a vectorial space and a geodesic distance in the Riemannian space of symmetric positive definite matrices. We showed that the geodesic distance provided a better classification of twins subjects, suggesting this use of this distance can robustly compare dynamic connectivity matrices.