  This paper introduces a clustering framework for networks with nodes
annotated with time-series data. The framework addresses all types of
network-clustering problems: State clustering, node clustering within states
(a.k.a. topology identification or community detection), and even
subnetwork-state-sequence identification/tracking. Via a bottom-up approach,
features are first extracted from the raw nodal time-series data by kernel
autoregressive-moving-average modeling to reveal non-linear dependencies and
low-rank representations, and then mapped onto the Grassmann manifold
(Grassmannian). All clustering tasks are performed by leveraging the underlying
Riemannian geometry of the Grassmannian in a novel way. To validate the
proposed framework, brain-network clustering is considered, where extensive
numerical tests on synthetic and real functional magnetic resonance imaging
(fMRI) data demonstrate that the advocated learning framework compares
favorably versus several state-of-the-art clustering schemes.
