A Hodge-FAST Framework for High-Resolution Dynamic Functional Connectivity Analysis of Higher Order Interactions in EEG Signals

TL;DR

This paper presents a novel Hodge-FAST framework that combines topological data analysis with dynamic connectivity filtering to analyze higher-order interactions in EEG signals, revealing new insights into Alzheimer-related MCI.

Contribution

The framework uniquely integrates Hodge decomposition with FAST connectivity to analyze transient, higher-order EEG interactions at high temporal resolution, addressing noise and sparsity.

Findings

Significant temporal differences in higher-order interactions in MCI patients

First high-resolution capture of higher-dimensional EEG interactions

Improved analysis of transient connectivity patterns

Abstract

We introduce a novel framework that integrates Hodge decomposition with Filtered Average Short-Term (FAST) functional connectivity to analyze dynamic functional connectivity (DFC) in EEG signals. This method leverages graph-based topology and simplicial analysis to explore transient connectivity patterns at multiple scales, addressing noise, sparsity, and computational efficiency. The temporal EEG data are first sparsified by keeping only the most globally important connections, instantaneous connectivity at these connections is then filtered by global long-term stable correlations. This tensor is then decomposed into three orthogonal components to study signal flows over higher-order structures such as triangle and loop structures. Our analysis of Alzheimer-related MCI patients show significant temporal differences related to higher-order interactions that a pairwise analysis on its own does not implicate. This allows us for the first time to capture higher-dimensional interactions at high temporal resolution in noisy EEG signal recordings.