Unraveling Temporal Dynamics of SPSD matrices viaRiemmanian Multi-Scale Decomposition

Abstract

Functional connectivity (FC) is fundamentally non-stationary, undergoing continuous reconfigurations that track shifting behavioral and cognitive states. Despite the importance of these transitions, existing analytical frameworks struggle to reconcile the high-dimensional nature of these reconfigurations with the need for structured trajectories and mechanistic interpretability. Specifically, identifying the precise network components responsible for driving these dynamics remains a significant challenge. To bridge this gap, we introduce RONI (Riemannian filtering Of Network Interactions), a geometry-aware, unsupervised framework that treats time-varying FC as a signal evolving on the manifold of symmetric positive semidefinite (SPSD) matrices. By defining intrinsic filtering operators along the SPSD geodesics, RONI enables a principled multiresolution decomposition of FC dynamics directly on the manifold. This representation allows for the isolation of "dynamic drivers" - specific network elements that dominate coherent connectivity modes across distinct temporal scales. We demonstrate the versatility of RONI by applying it to a diverse array of large-scale neural recordings, including hippocampal electrophysiology data, cortex-wide and dendritic calcium imaging, and human EEG. Across these varied modalities and spatio-temporal scales, RONI identifies biologically meaningful sub-networks that shape the geometry of the connectivity trajectory, providing a unified, interpretable, and quantitative framework for studying the evolution of distributed neural interactions.