Robust State-space Reconstruction of Brain Dynamics via Bootstrap Monte Carlo SSA

Abstract

Reconstructing latent state-space geometry from time series provides a powerful route to studying nonlinear dynamics across complex systems. Delay-coordinate embedding provides the theoretical basis but assumes long, noise-free recordings, which many domains violate. In many real-world domains, recordings are short, noisy, and coarsely sampled; in neuroimaging, for example, fMRI additionally contains autocorrelated background structure that can obscure oscillatory components and destabilize embeddings. We propose bootstrap Monte Carlo singular spectrum analysis (BMC-SSA), which combines Monte Carlo SSA with bootstrap stability to retain oscillatory modes that are statistically supported and reproducible across resampled data. This produces reconstructions that emphasize reliable oscillatory structure, enhancing determinism and stabilizing subsequent embeddings. Our results show that BMC-SSA improves the reliability of functional measures and uncovers differences in state-space dynamics in fMRI, offering a general framework for robust embedding of noisy, finite signals.