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

TL;DR

This paper presents a novel framework for clustering networks with time-series data, using kernel-ARMA modeling and Grassmannian geometry, validated on brain-network data with promising results.

Contribution

It introduces a new clustering approach combining kernel-ARMA features and Grassmannian geometry, applicable to various network clustering problems.

Findings

Outperforms several state-of-the-art clustering methods on synthetic data.

Effective in brain-network clustering with real fMRI data.

Handles diverse clustering tasks within a unified framework.

Abstract

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.