Unifying equivalences across unsupervised learning, network science, and imaging/network neuroscience

Area of Science:

• Integrative data science
• Network science
• Neuroscience

Background:

• Modern science struggles with integrating vast data, risking circular analyses and redundancy.
• Previous work highlighted the negative consequences of neglecting data integration.

Purpose of the Study:

• To advance scientific integration by describing equivalences across diverse analytical methods.
• To unify analyses in unsupervised learning, network science, and neuroscience.

Main Methods:

• Equating foundational objectives in unsupervised learning (e.g., k-means, UMAP) and network science (e.g., modularity).
• Fusing classic algorithms for objective optimization and extending them for dimensionality reduction interpretation.
• Equating network centrality and dynamics measures with communication, control, and diversity metrics.
• Developing semi-analytical vignettes for interpreting structural and dynamical brain imaging data.

Main Results:

• Demonstrated equivalences unifying clustering, dimensionality reduction, network centrality, and dynamics.
• Provided simplified interpretations for popular dimensionality reduction and network neuroscience models.
• Illustrated findings using brain-imaging data and introduced the open-source 'abct' toolbox.

Conclusions:

• The study successfully unifies diverse analytical approaches across multiple scientific domains.
• The findings facilitate more integrated and less redundant scientific explanations.
• The 'abct' toolbox supports the practical application of these unifying analyses.