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Register a new userGraph Signal Processing over Multilayer Networks -- Part I: Foundations and Spectrum Analysis
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Added by
Songyang Zhang
Publication date
2021
fields
Electronic Engineering
and research's language is
English
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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 interactions among distinct entities. Such complex interactions may represent multiple levels of interactions that are difficult to be modeled with a single layer graph and can instead be captured by multiple layers of graph connections. Such multilayer/multi-level data structure can be more naturally modeled and captured by a high-dimensional multi-layer network (MLN). This work generalizes traditional graph signal processing (GSP) over multilayer networks for analysis of such multilayer signal features and their interactions. We propose a tensor-based framework of this multilayer network signal processing (M-GSP) in this two-part series. Specially, Part I introduces the fundamentals of M-GSP and studies spectrum properties of MLN Fourier space. We further describe its connections to traditional digital signal processing and GSP. Part II focuses on several major tools within the M-GSP framework for signal processing and data analysis. We provide results to demonstrate the efficacy and benefits of applying multilayer networks and the M-GSP in practical scenarios.
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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, this second Part focuses on more detailed discussions of implementation and applications of M-GSP. Specifically, we define the concepts of stationary process, convolution, bandlimited signals, and sampling theory over multilayer networks. We also develop fundamentals of filter design and derive approximated methods of spectrum estimation within the proposed framework. For practical applications, we further present several MLN-based methods for signal processing and data analysis. Our experimental results demonstrate significant performance improvement using our M-GSP framework over traditional signal processing solutions.
In a networked system, functionality can be seriously endangered when nodes are infected, due to internal random failures or a contagious virus that develops into an epidemic. Given a snapshot of the network representing the nodes states (infected or healthy), infection analysis refers to distinguishing an epidemic from random failures and gathering information for effective countermeasure design. This analysis is challenging due to irregular network structure, heterogeneous epidemic spreading, and noisy observations. This paper treats a network snapshot as a graph signal, and develops effective approaches for infection analysis based on graph signal processing. For the macro (network-level) analysis aiming to distinguish an epidemic from random failures, 1) multiple detection metrics are defined based on the graph Fourier transform (GFT) and neighborhood characteristics of the graph signal; 2) a new class of graph wavelets, distance-based graph wavelets (DBGWs), are developed; and 3) a machine learning-based framework is designed employing either the GFT spectrum or the graph wavelet coefficients as features for infection analysis. DBGWs also enable the micro (node-level) infection analysis, through which the performance of epidemic countermeasures can be improved. Extensive simulations are conducted to demonstrate the effectiveness of all the proposed algorithms in various network settings.
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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