Spectral Topological Data Analysis of Brain Signals

TL;DR

This paper introduces spectral TDA (STDA), a novel method that uses spectral domain dependence measures to analyze brain connectivity, providing detailed topological summaries that reveal frequency-specific differences in EEG data between ADHD patients and controls.

Contribution

The paper develops a frequency-specific topological data analysis approach using coherence, creating the spectral landscape for detailed brain network analysis, which improves upon simplistic connectivity measures.

Findings

Spectral landscape captures nuanced brain connectivity features.

Frequency-specific topological differences identified between ADHD and controls.

STDA provides a more detailed understanding of brain network topology.

Abstract

Topological data analysis (TDA) has become a powerful approach over the last twenty years, mainly due to its ability to capture the shape and the geometry inherent in the data. Persistence homology, which is a particular tool in TDA, has been demonstrated to be successful in analyzing functional brain connectivity. One limitation of standard approaches is that they use arbitrarily chosen threshold values for analyzing connectivity matrices. To overcome this weakness, TDA provides a filtration of the weighted brain network across a range of threshold values. However, current analyses of the topological structure of functional brain connectivity primarily rely on overly simplistic connectivity measures, such as the Pearson orrelation. These measures do not provide information about the specific oscillators that drive dependence within the brain network. Here, we develop a frequency-specific approach that utilizes coherence, a measure of dependence in the spectral domain, to evaluate the functional connectivity of the brain. Our approach, the spectral TDA (STDA), has the ability to capture more nuanced and detailed information about the underlying brain networks. The proposed STDA method leads to a novel topological summary, the spectral landscape, which is a 2D-generalization of the persistence landscape. Using the novel spectral landscape, we analyze the EEG brain connectivity of patients with attention deficit hyperactivity disorder (ADHD) and shed light on the frequency-specific differences in the topology of brain connectivity between the controls and ADHD patients.