Network clustering via kernel-ARMA modeling and the Grassmannian: The brain-network case

This paper demonstrates that all clustering tasks in a dynamic (brain) network, i.e., state clustering, community detection, and subnetwork state-sequence clustering, can be addressed by a novel unifying network-clustering framework. The connecting threads of the components of the proposed framework are: a novel kernel-based autoregressive-moving-average (ARMA) model which propels feature extraction from the network time-series, and the Riemannian geometry of the Grassmann manifold (Grassmannian) into which the extracted features are mapped. Clustering of the Grassmannian features is performed via the novel extension of a recently introduced algorithm which capitalizes on the Grassmannian distances and angular information of the point-cloud of features. Numerical tests on synthetic and real functional-magnetic-resonance-imaging (fMRI) data showcase the favorable performance of the proposed scheme against state-of-the-art network-clustering and manifold-learning methods, and corroborate the claim of this paper that the proposed framework can serve as a useful data-analytic toolbox for network(-neuroscience) research.