# Brain-Network Clustering via Kernel-ARMA Modeling and the Grassmannian

## TL;DR

This paper introduces a novel brain-network clustering method using kernel-ARMA modeling and Grassmannian geometry, effectively capturing non-linear dependencies and unifying various clustering tasks in brain data analysis.

## Contribution

It proposes a new feature-extraction approach via kernel ARMA models and a unifying clustering framework on the Grassmann manifold for diverse brain-network clustering problems.

## Key findings

- Outperforms several state-of-the-art clustering schemes on synthetic data.
- Effectively captures non-linear nodal dependencies in brain networks.
- Successfully applied to real fMRI and EEG data with promising results.

## 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.