Time-varying Graph Signal Estimation via Dynamic Multi-hop Topologies

The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among time-varying node signals, while also accounting for time-varying edge signals, by extracting latent edges through topological diffusion and edge pruning. The resulting graphs are time-varying and sparse, capturing key dynamic node interactions and representing signal diffusion to both near and distant neighbors over time. The Dynamic Multi-hop Estimation algorithm is further proposed, accurately representing the interaction dynamics among node signals while enabling adaptive estimation of time-varying multivariate signals spatially and temporally. The Dynamic Multi-hop Estimation is evaluated under two real-world datasets of brain network and stock market for the online estimation of partially observed time-varying signals corrupted by noise.

Sequential Monte Carlo Graph Convolutional Network for Dynamic Brain Connectivity

An increasingly important brain function analysis modality is functional connectivity analysis which regards connections as statistical codependency between the signals of different brain regions. Graph-based analysis of brain connectivity provides a new way of exploring the association between brain functional deficits and the structural disruption related to brain disorders, but the current implementations have limited capability due to the assumptions of noise-free data and stationary graph topology. We propose a new methodology based on the particle filtering algorithm, with proven success in tracking problems, which estimates the hidden states of a dynamic graph with only partial and noisy observations, without the assumptions of stationarity on connectivity. We enrich the particle filtering state equation with a graph Neural Network called Sequential Monte Carlo Graph Convolutional Network (SMC-GCN), which due to the nonlinear regression capability, can limit spurious connections in the graph. Experiment studies demonstrate that SMC-GCN achieves the superior performance of several methods in brain disorder classification.