Identification of Local Neighbourhoods in a Network for Graph-based Signal Reconstruction

Abstract

The Internet of Things (IoT) relies heavily on exchange of data collected by nodes in a sensor network. This network data can be represented as a signal on a graph allowing tools from graph signal processing (GSP) to analyse it. Here, we utilize graph signal reconstruction algorithms to extrapolate missing sensor data from partially sampled network data. An important class of graph signal reconstruction algorithms operate by partitioning the graph vertices into local sets to achieve lower reconstruction errors and faster convergence. However, methods for identification of these local neighbourhoods have not been clearly studied in the literature. Here, we propose two flexible algorithms to generate local sets on a graph. These algorithms are based on the distance between the sampled and unsampled vertices. Our algorithms are competitive with the methods in literature while offering flexibility in the number of sampled vertices. We carry out simulation-based analysis of sampling strategies and proposed local set generation algorithms using local-set-based reconstruction algorithms.