Clustering brain-network-connectivity states using kernel partial correlations

In response to the demand on data-analytic tools that monitor time-varying connectivity patterns within brain networks, the present paper extends the framework of [Slavakis et al., SSP'16] to include kernel-based partial correlations as a tool for clustering dynamically evolving connectivity states of networks. Such an extension becomes feasible due to the argument which runs beneath also this work: network dynamics can be successfully captured if learning is performed in Rie-mannian manifolds. Sequences of kernel-based partial correlations, collected over time and across a network, are mapped to sequences of points in the Riemannian manifold of positive-(semi)definite matrices, and a sequence that corresponds to a specific connected state of the network forms a submanifold or cluster. Based on a very recently developed line of research, this work demonstrates that by exploiting Riemannian geometry in a specific way, the present clustering framework outperforms classical and state-of-the-art techniques on segmenting connectivity states, observed from both synthetic and real brain-network data.