Graphon Signal Processing

Ruiz, Luana; Chamon, Luiz F. O.; Ribeiro, Alejandro

doi:10.1109/tsp.2021.3106857

Cited by 31 publications

(47 citation statements)

References 43 publications

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“…Having reduced the moments of the normalized power spectral distribution to an average over the distribution of rooted balls, we can now reason about the convergence of graph Fourier distributions in terms of weak convergence of measure for graphs with bounded degree D. Although the limit of dense graphs has been considered before via graphon models [29,30], this cannot capture the behavior of bounded degree graphs, as all infinite sequences of growing graphs of bounded degree converge to the zero graphon [31]. However, in the case of sparse graphs, understanding the descension of maps to the space Ω K is a feasible approach, with the following compactness property.…”

Section: Power Spectral Densitymentioning

confidence: 99%

On Local Distributions in Graph Signal Processing

Roddenberry,

Gama,

Baraniuk

et al. 2022

Preprint

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Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local neighborhood of each node. Moreover, a graph filter's output can be computed separately at each node by carrying out repeated exchanges with immediate neighbors. Graph filters can be compactly written as polynomials of a graph shift operator (typically, a sparse matrix description of the graph). This has led to relating the properties of the filters with the spectral properties of the corresponding matrixwhich encodes global structure of the graph. In this work, we propose a framework that relies solely on the local distribution of the neighborhoods of a graph. The crux of this approach is to describe graphs and graph signals in terms of a measurable space of rooted balls. Leveraging this, we are able to seamlessly compare graphs of different sizes and coming from different models, yielding results on the convergence of spectral densities, transferability of filters across arbitrary graphs, and continuity of graph signal properties with respect to the distribution of local substructures.

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Section: Power Spectral Densitymentioning

confidence: 99%

On Local Distributions in Graph Signal Processing

Roddenberry,

Gama,

Baraniuk

et al. 2022

Preprint

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“…The frequency response of h in ( 12) is computed with (5). For the filter in (12), the result is shown in Fig.…”

Section: Examplementioning

confidence: 99%

“…Thus, there have been various recent works that aim to further broaden SP beyond graphs. Examples include SP on hypergraphs [4], graphons [5], simplicial complexes [6], so-called quivers [7], and powersets [8]. Some of the above works have been inspired by the algebraic signal processing theory (ASP) [9], [10], which provides the axioms and a general approach to obtaining new SP frameworks.…”

Section: Introductionmentioning

confidence: 99%

Discrete Signal Processing on Meet/Join Lattices

Püschel

Seifert

Wendler

2021

IEEE Trans. Signal Process.

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A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains including social data analysis, natural language processing, computational chemistry and biology, and database theory. In this paper we introduce discretelattice signal processing (DLSP), an SP framework for data, or signals, indexed by such lattices. We use the meet (or join) to define a shift operation and derive associated notions of filtering, Fourier basis and transform, and frequency response. We show that the spectrum of a lattice signal inherits the lattice structure of the signal domain and derive a sampling theorem. Finally, we show two prototypical applications: spectral analysis of formal concept lattices in social science and sampling and Wiener filtering of multiset lattices in combinatorial auctions. Formal concept lattices are a compressed representation of relations between objects and attributes. Since relations are equivalent to bipartite graphs and hypergraphs, DLSP offers a form of Fourier analysis for these structures.

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“…The area of graph signal processing (GSP) has received extensive attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Graph signal processing has been found in social and economic networks, climate analysis, traffic patterns, marketing preferences, and so on [19][20][21][22][23][24][25][26].…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%

Robust Adaptive Estimation of Graph Signals Based on Welsch Loss

Wang

Sun

2022

Symmetry

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This paper considers the problem of adaptive estimation of graph signals under the impulsive noise environment. The existing least mean squares (LMS) approach suffers from severe performance degradation under an impulsive environment that widely occurs in various practical applications. We present a novel adaptive estimation over graphs based on Welsch loss (WL-G) to handle the problems related to impulsive interference. The proposed WL-G algorithm can efficiently reconstruct graph signals from the observations with impulsive noises by formulating the reconstruction problem as an optimization based on Welsch loss. An analysis on the performance of the WL-G is presented to develop effective sampling strategies for graph signals. A novel graph sampling approach is also proposed and used in conjunction with the WL-G to tackle the time-varying case. The performance advantages of the proposed WL-G over the existing LMS regarding graph signal reconstruction under impulsive noise environment are demonstrated.

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Graphon Signal Processing

Cited by 31 publications

References 43 publications

On Local Distributions in Graph Signal Processing

On Local Distributions in Graph Signal Processing

Discrete Signal Processing on Meet/Join Lattices

Robust Adaptive Estimation of Graph Signals Based on Welsch Loss

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