A Wavelet Lifting Approach for Representing and Denoising Functions on Network Edges

Data collected over networks arise in a number of scientific, engineering and industrial applications, in which the datapoints are noisy observations relating to a process of interest over the graph structure. In this article we propose a novel multiscale representation of data on the edges of a network. In contrast to other methods in the literature which employ expensive node to edge data transformations, our decomposition acts directly on the network edges. Using our method, we propose an efficient edge denoising algorithm, termed E-LOCAAT, which displays good performance across a range of data scenarios, particularly when the number of edges is large. The proposed method is illustrated using extensive simulations and we demonstrate its applicability on a real-world dataset arising in road traffic modeling.