Clustering time varying connectivity networks by riemannian geometry: The brain network case
In response to the demand on data analytic tools that monitor time varying connectivity patterns within brain networks, the present paper introduces a framework for clustering (unsupervised learning) of dynamically evolving connectivity states of networks. This work advocates learning of network dynamics on Riemannian manifolds, capitalizing on the well known fact that popular features in statistics enjoy that structure: (Partial) correlations or covariances can be mapped to the manifold of positive (semi )definite symmetric matrices, while low rank linear subspaces can be considered as points of the Grassmannian. Sequences of such features, collected over time and across a network, are mapped to sequences of points on a Riemannian manifold, and a sequence that corresponds to a specific state of the network forms a cluster or submanifold. Geometry is exploited in a novel way to demonstrate the rich potential of the proposed learning method for monitoring time varying network patterns by outperforming state of the art techniques on synthetic brain network data.
2016 IEEE Statistical Signal Processing Workshop (SSP)