Adaptive Gaussian graph-spectral filtering for scale-specific connectivity inference

Functional connectivity changes in neurodegeneration involve not only regional disconnection but also scale-specific reorganization of brain networks. We introduce the Multiscale Spectral Gaussian Filtering (MSGauF) framework, which transforms each subject's Laplacian spectrum into a data-driven coordinate system for connectivity analysis. MSGauF defines adaptive frequency bands from spectral changepoints, and within each band, normalized similarity measures enable sign-separated, cluster-level permutation testing without requiring eigenvector alignment. Simulations show improved precision when connectivity changes are confined to specific spectral ranges. Applied to resting-state fMRI from Alzheimer's and Parkinson's cohorts, the method revealed distinct spectral signatures of disease. In Alzheimer's disease, connectivity shifted from large-scale attenuation in mild impairment to fine-scale polarity reversal, reflecting disrupted long-range inhibition and local hyperexcitability. In Parkinson's disease, polarity was preserved but spectrally compressed, indicating reduced flexibility and rigid synchronization of local circuits. These findings highlight the advantages of frequency-resolved analysis in revealing structured, multiscale connectivity changes that are missed by conventional broadband approaches.