Distributed adaptive learning of graph processes via in-network subspace projections

In this paper, we introduce a novel adaptive method for distributed recovery of graph processes, which are observed over a dynamic set of vertices. The proposed algorithm hinges on proximal gradient optimization techniques, while leveraging in-network projections as a mechanism to enforce graph bandwidth constraints in a cooperative and distributed fashion, and thresholding operators to identify anomalous sparse components hidden in the signals. The theoretical analysis illustrates the mean-square stability of the proposed adaptive method. Finally, numerical tests on synthetic and real data assess the performance of the proposed distributed strategy for adaptive learning of graph processes.