Modeling Sparse Graph Sequences and Signals Using Generalized Graphons

IF 4.6 2区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
Feng Ji;Xingchao Jian;Wee Peng Tay
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引用次数: 0

Abstract

Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach is that any sparse sequence of graphs inevitably converges to the zero graphon, rendering the resulting signal processing theory trivial and inadequate for sparse graph sequences. To overcome this limitation, we propose a new signal processing framework that leverages the concept of generalized graphons and introduces the stretched cut distance as a measure to compare these graphons. Our framework focuses on the sampling of graph sequences from generalized graphons and explores the convergence properties of associated operators, spectra, and signals. Our signal processing framework provides a comprehensive approach to analyzing and processing signals on graph sequences, even if they are sparse. Finally, we discuss the practical implications of our theory for real-world large networks through numerical experiments.
使用广义图元对稀疏图序列和信号建模
图元是图序列的极限对象,用于分析大型图的行为。最近,人们开发了图元信号处理方法来研究大型图上的信号处理。这种方法的一个主要局限是,任何稀疏的图序列都不可避免地收敛于零图元,从而使由此产生的信号处理理论变得琐碎,不足以用于稀疏图序列。为了克服这一局限,我们提出了一种新的信号处理框架,利用广义图元的概念,并引入拉伸切割距离作为比较这些图元的度量。我们的框架侧重于从广义图元对图序列进行采样,并探索相关算子、频谱和信号的收敛特性。我们的信号处理框架为分析和处理图序列上的信号提供了一种全面的方法,即使这些信号是稀疏的。最后,我们通过数值实验讨论了我们的理论对现实世界大型网络的实际意义。
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来源期刊
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing 工程技术-工程:电子与电气
CiteScore
11.20
自引率
9.30%
发文量
310
审稿时长
3.0 months
期刊介绍: The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.
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