riemtan, riemstats: R packages for Riemannian geometry techniques in the analysis of multiple samples of connectomes

Abstract

Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some tools for SPD matrix analysis, they suffer from limitations in scalability, numerical stability, and metric flexibility that hinder their application to modern large-scale connectomics studies. We present riemtan, a comprehensive R package that addresses these challenges through a unified, high-level interface supporting multiple Riemannian metrics, efficient parallel computation, and seamless conversion between manifold, tangent, and vectorized representations. Building on riemtan's foundation, we also introduce riemstats, which implements advanced statistical methods including Fr\'echet ANOVA, Riemannian ANOVA with classic test statistics, and harmonization techniques for multi-site studies. The modular design facilitates integration with existing R workflows and provides an extensible framework for future methodological developments in manifold-valued data analysis.