No abstract

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.

This paper introduces a clustering framework for networks with nodes are annotated with time-series data. The framework addresses all types of networkclustering 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, brainnetwork 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-ofthe-art clustering schemes.