Topological Distances Between Brain Networks

Area of Science:

• Neuroscience
• Network Science
• Data Analysis

Background:

• Existing brain network distances often rely on matrix norms, which can overlook topological distinctions.
• Matrix norms are susceptible to outliers, potentially skewing distance calculations due to extreme edge weights.
• There is a need for novel network distance metrics that accurately reflect network topology.

Purpose of the Study:

• Introduce and evaluate Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances for brain network analysis.
• Compare the performance of KS-distance against traditional matrix norms and GH-distance.
• Apply KS-distance to characterize brain networks in a multimodal neuroimaging study.

Main Methods:

• Utilized Gromov-Hausdorff (GH) distance, a metric often employed in persistent homology for brain networks.
• Introduced and evaluated Kolmogorov-Smirnov (KS) distance for its ability to capture topological features.
• Conducted simulations comparing KS-distance, GH-distance, and matrix norms against ground truth random networks.
• Applied KS-distance to analyze multimodal MRI and DTI data from maltreated children.

Main Results:

• KS-distance demonstrated superior performance compared to matrix norms and GH-distance in simulations.
• The study highlights the limitations of matrix norms in capturing topological differences in brain networks.
• KS-distance proved effective in characterizing brain network alterations in maltreated children.

Conclusions:

• KS-distance offers a more robust and topologically sensitive measure for brain network comparison.
• The findings suggest KS-distance as a valuable tool for neuroimaging research, particularly in clinical populations.
• This work advances the methodology for analyzing complex brain network structures.