Graph-adaptive semi-supervised tracking of dynamic processes over switching network modes

A plethora of network-science related applications call for inference of spatio-temporal graph processes. Such an inference task can be aided by the underlying graph topology that might jump over discrete modes. For example, the connectivity in dynamic brain networks, switches among candidate topologies, each corresponding to a different emotional state, also known as the network mode. Taking advantage of limited nodal observations, the present contribution deals with semi-supervised tracking of dynamic processes over a given candidate set of graphs with unknown switches. Towards this end, a dynamical model is introduced to capture the per-slot spatial correlation using the active topology, as well as the temporal variation across slots through a state-space model. A scalable graph-adaptive Bayesian approach is developed, based on what is termed interacting multi-graph model (IMGM), to track the dynamic nodal processes and the active graph topology on-the-fly. Besides switching topologies, the proposed IMGM algorithm can accommodate various generalizations, including multiple dynamic functions, multiple kernels, and adaptive observation noise covariances. IMGM learns the dynamical model that best fits the data from a pool of available models. Thus, the resultant adaptive algorithm does not require offline model training. Numerical tests with synthetic and real datasets demonstrate the superior tracking performance of the novel approach compared to the mode-clairvoyant existing alternatives.