Advances in Distributed Graph Filtering

Abstract: Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this work generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize the subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parametrization the proposed graph filters provide insights in approximating linear operators through the succession and composition of local operators, i.e., fixed support matrices, which span applications beyond the field of graph signal processing. A set of numerical results shows the benefits of the edge-variant filters over current methods and illustrates their potential to a wider range of applications than graph filtering.