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Graph signal processing (GSP) is an emerging field developed for analyzing signals defined on irregular spatial structures modeled as graphs. Given the considerable literature regarding the resilience of infrastructure networks using graph theory, it is not surprising that a number of applications of GSP can be found in the resilience domain. GSP techniques assume that the choice of graphical Fourier transform (GFT) imparts a particular spectral structure on the signal of interest. We assess a number of power distribution systems with respect to metrics of signal structure and identify several correlates to system properties and further demonstrate how these metrics relate to performance of some GSP techniques. We also discuss the feasibility of a data-driven approach that improves these metrics and apply it to a water distribution scenario. Overall, we find that many of the candidate systems analyzed are properly structured in the chosen GFT basis and amenable to GSP techniques, but identify considerable variability and nuance that merits future investigation.
Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying graph stru
Collective motion among biological organisms such as insects, fish, and birds has motivated considerable interest not only in biology but also in distributed robotic systems. In a robotic or biological swarm, anomalous agents (whether malfunctioning
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the standard approaches of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical structure used
Signal processing over single-layer graphs has become a mainstream tool owing to its power in revealing obscure underlying structures within data signals. For generally, many real-life datasets and systems are characterized by more complex interactio
This work introduces a tensor-based framework of graph signal processing over multilayer networks (M-GSP) to analyze high-dimensional signal interactions. Following Part Is introduction of fundamental definitions and spectrum properties of M-GSP, thi