Interpretable Multiscale Reconstruction of Correlation-Matrix Dynamics

This project builds on our prior work on the dynamics of symmetric positive definite (SPD) matrices in time-varying functional connectivity, where we introduced RONI – a geometric multiresolution decomposition, analogous to an analysis filter bank based on the Haar wavelet. By decomposing connectivity time series into components across multiple temporal scales, this framework enables principled identification of dominant drivers of network dynamics while explicitly respecting the intrinsic geometry of correlation matrices.

Here, we develop the complementary synthesis framework: an optimal reconstruction methodology that defines the inverse of the geometric filtering operations, thereby making the transform fully reversible. This extension moves RONI beyond one-way analysis and enables controlled signal synthesis by selectively recombining scale-specific components, supporting denoising, trajectory isolation, and hypothesis-driven manipulation of network dynamics. We further introduce new interpretability methods that connect reconstructed components to meaningful dynamical mechanisms, providing transparent, geometry-preserving explanations of how multiscale features contribute to observed connectivity changes.