  Recent advances in neuroscience and in the technology of functional magnetic
resonance imaging (fMRI) and electro-encephalography (EEG) have propelled a
growing interest in brain-network clustering via time-series analysis.
Notwithstanding, most of the brain-network clustering methods revolve around
state clustering and/or node clustering (a.k.a. community detection or topology
inference) within states. This work answers first the need of capturing
non-linear nodal dependencies by bringing forth a novel feature-extraction
mechanism via kernel autoregressive-moving-average modeling. The extracted
features are mapped to the Grassmann manifold (Grassmannian), which consists of
all linear subspaces of a fixed rank. By virtue of the Riemannian geometry of
the Grassmannian, a unifying clustering framework is offered to tackle all
possible clustering problems in a network: Cluster multiple states, detect
communities within states, and even identify/track subnetwork state sequences.
The effectiveness of the proposed approach is underlined by extensive numerical
tests on synthetic and real fMRI/EEG data which demonstrate that the advocated
learning method compares favorably versus several state-of-the-art clustering
schemes.
