Higher-order statistics for constructing centered edge functional connectivity

Area of Science:

• Neuroscience
• Network Science
• Computational Biology

Background:

• Functional connectivity analysis is crucial for understanding neural systems, typically using correlations between brain regions.
• Traditional methods may miss complex, higher-order relationships.
• Edge-centric functional connectivity (eFC) offers a new perspective but can be biased by including mean edge time series values.

Purpose of the Study:

• To propose a novel, unbiased method for estimating covariation between pairs of edges in brain networks.
• To introduce centered edge functional connectivity (ceFC) as an improvement over existing eFC methods.
• To develop statistical frameworks for evaluating and refining ceFC estimations.

Main Methods:

• Developed centered edge functional connectivity (ceFC) to estimate unbiased covariation between edge pairs.
• Established theoretical foundations for ceFC consistency with sufficient sample sizes.
• Created a multiple hypothesis testing framework with false discovery rate control.
• Implemented thresholding for high-dimensional settings where nodes exceed samples.

Main Results:

• The proposed ceFC estimator is theoretically consistent.
• The multiple hypothesis testing framework effectively evaluates unbiased covariation strength.
• Thresholded ceFC estimators converge to the true ceFC matrix in high-dimensional scenarios.
• Numerical studies and a real-world dataset (Midnight Scan Club) validated the methods' performance.

Conclusions:

• ceFC provides a statistically sound and unbiased approach to analyzing higher-order interactions in brain networks.
• The developed statistical framework enhances the reliability of network analysis.
• This work offers a valuable tool for advancing the understanding of neural system organization.