Regression and alignment for functional data and network topology.

Area of Science:

• Neuroscience
• Network Science
• Graph Theory

Background:

• Brain functional connections form complex networks analyzed using graph theory.
• Network diagnostics like modularity change during childhood and adolescence.
• Previous studies often use arbitrary preprocessing parameters, potentially biasing results.

Purpose of the Study:

• To develop a method that avoids arbitrary parameter choices in network analysis.
• To investigate the relationship between developmental changes in functional brain networks and cognitive performance.
• To improve the interpretability and generalizability of network neuroscience studies.

Main Methods:

• Conceptualizing network diagnostics as functions of preprocessing parameters, creating diagnostic curves.
• Utilizing scalar-on-function regression to relate network curves to cognitive function and other covariates.
• Proposing a supervised curve alignment method to handle systematic network differences and incorporate auxiliary data.

Main Results:

• Network diagnostic curves capture topology across multiple scales, offering a more comprehensive view than single values.
• The proposed scalar-on-function regression and curve alignment methods provide a flexible framework for analyzing heterogeneous network data.
• The iterative optimization algorithm effectively performs both functional regression and alignment.

Conclusions:

• This approach offers a robust alternative to arbitrary parameter selection in network neuroscience.
• The method enhances the ability to study developmental changes in brain networks and their link to cognition.
• The developed techniques have the potential to advance the interpretability and applicability of connectome research.