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Register a new userGraph Signal Processing of Indefinite and Complex Graphs using Directed Variation
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Added by
Kevin Schultz
Publication date
2020
fields
Electronic Engineering
and research's language is
English
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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 in fields such as neuroscience, critical infrastructure, and robot coordination, further complicates the issue. Recent results generalized the total variation of a graph signal to that of directed variation as a motivating principle for developing a graphical Fourier transform (GFT). Here, we extend these techniques to concepts of signal variation appropriate for indefinite and complex-valued graphs and use them to define a GFT for these classes of graph. Simulation results on random graphs are presented, as well as a case study of a portion of the fruit fly connectome.
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Smart grids are large and complex cyber physical infrastructures that require real-time monitoring for ensuring the security and reliability of the system. Monitoring the smart grid involves analyzing continuous data-stream from various measurement devices deployed throughout the system, which are topologically distributed and structurally interrelated. In this paper, graph signal processing (GSP) has been used to represent and analyze the power grid measurement data. It is shown that GSP can enable various analyses for the power grids structured data and dynamics of its interconnected components. Particularly, the effects of various cyber and physical stresses in the power grid are evaluated and discussed both in the vertex and the graph-frequency domains of the signals. Several techniques for detecting and locating cyber and physical stresses based on GSP techniques have been presented and their performances have been evaluated and compared. The presented study shows that GSP can be a promising approach for analyzing the power grids data.
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in an efficient way on graphs. We investigate how PUMs can be combined with a local graph basis function (GBF) approximation method in order to obtain low-cost global interpolation or classification schemes. From a theoretical point of view, we study necessary prerequisites for the partition of unity such that global error estimates of the PUM follow from corresponding local ones. Finally, properties of the PUM as cost-efficiency and approximation accuracy are investigated numerically.
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 structure, as in social, biological, and many other domains. This paper explores 1)how graph signal processing (GSP) can be used to extend CNN components to graphs in order to improve model performance; and 2)how to design the graph CNN architecture based on the topology or structure of the data graph.
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 or nefarious) behave differently than the normal agents and attempt to hide in the chaos of the swarm. By defining a graph structure between agents in a swarm, we can treat the agents properties as a graph signal and use tools from the field of graph signal processing to understand local and global swarm properties. Here, we leverage this idea to show that anomalous agents can be effectively detected using their impacts on the graph Fourier structure of the swarm.
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.
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