Online learning of time-varying signals and graphs

The aim of this paper is to propose a method for online learning of time-varying graphs from noisy observations of smooth graph signals collected over the vertices. Starting from an initial graph, and assuming that the topology can undergo the perturbation of a small percentage of edges over time, the method is able to track the graph evolution by exploiting a small perturbation analysis of the Laplacian matrix eigendecomposition, while assuming that the graph signal is bandlimited. The proposed method alternates between estimating the time-varying graph signal and recovering the dynamic graph topology. Numerical results corroborate the effectiveness of the proposed learning strategy in the joint online recovery of graph signal and topology.