Graph-Aided Multivariate Signal Decomposition

This work addresses the challenge of decomposing time-varying graph signals into their constituent amplitude- and frequency-modulated components while inferring their dynamic functional connectivity structures, known as graph mode decomposition (GMD). The existing method within the graph signal processing (GSP) framework yields static connectivity structures, limiting its real-life applicability and relying heavily on the user-defined parameter of the total number of existing modes in the signal K. We present a novel method to overcome these limitations, offering dynamic multi-scale connectivity structures and amplitude-frequency components. The approach formulates a variational optimization problem, integrating a prior for time-varying edge weights, and employs a successive scheme for optimization, eliminating the need for a priori specification of the number of components K. The performance of the method is validated on both synthetic and real datasets.