Topological data analysis of human brain networks through order statistics

Area of Science:

• Neuroscience
• Network Science
• Topology

Background:

• Understanding human brain network topology is crucial for comprehending brain functions.
• Representing the human connectome as a graph aids in analyzing brain network properties.
• Group-level statistical inference for brain graphs, considering heterogeneity and randomness, remains challenging.

Purpose of the Study:

• To develop a robust statistical framework for analyzing brain networks using persistent homology and order statistics.
• To simplify the computation of persistent barcodes in brain graph analysis.
• To identify topological differences in brain networks between sexes.

Main Methods:

• A novel statistical framework was developed based on persistent homology.
• Order statistics were employed to simplify the computation of persistent barcodes.
• The framework was validated through comprehensive simulation studies.
• The method was applied to resting-state functional magnetic resonance imaging data.

Main Results:

• The proposed method successfully analyzed brain network topology.
• Order statistics significantly simplified the computation of persistent barcodes.
• Statistically significant topological differences were identified between male and female brain networks.

Conclusions:

• The developed persistent homology framework with order statistics offers a robust approach for brain network analysis.
• This method can reveal subtle topological distinctions, such as sex-based differences in brain networks.
• The findings contribute to a deeper understanding of brain network organization and function.