Network Clustering Via Kernel-ARMA Modeling and the Grassmannian The Brain-Network Case

Abstract

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.