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We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…

Data Structures and Algorithms · Computer Science 2010-07-22 Daniel A. Spielman , Shang-Hua Teng

Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert…

Machine Learning · Computer Science 2024-05-22 Keke Huang , Yu Guang Wang , Ming Li , and Pietro Liò

This paper proposes a scalable algorithmic framework for spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original…

Data Structures and Algorithms · Computer Science 2018-12-24 Zhiqiang Zhao , Yongyu Wang , Zhuo Feng

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that,…

Machine Learning · Computer Science 2021-04-07 Filippo Maria Bianchi , Daniele Grattarola , Lorenzo Livi , Cesare Alippi

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…

Anomaly detection in networks often boils down to identifying an underlying graph structure on which the abnormal occurrence rests on. Financial fraud schemes are one such example, where more or less intricate schemes are employed in order…

Machine Learning · Computer Science 2022-06-10 Andra Baltoiu , Andrei Patrascu , Paul Irofti

We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…

Signal Processing · Electrical Eng. & Systems 2025-07-28 Giacomo Elefante , Gianluca Giacchi , Michael Multerer , Jacopo Quizi

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…

Machine Learning · Computer Science 2025-09-29 Snir Hordan , Maya Bechler-Speicher , Gur Lifshitz , Nadav Dym

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…

Signal Processing · Electrical Eng. & Systems 2023-12-18 Luana Ruiz , Luiz F. O. Chamon , Alejandro Ribeiro

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Data Structures and Algorithms · Computer Science 2017-02-01 Richard Peng , He Sun , Luca Zanetti

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…

Information Theory · Computer Science 2014-11-13 Ilan Shomorony , A. Salman Avestimehr

Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications, for instance in statistical or deep learning, using frames built from graphs, such as wavelets on graphs,…

Signal Processing · Electrical Eng. & Systems 2023-03-08 Elie Chedemail , Basile de Loynes , Fabien Navarro , Baptiste Olivier

We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…

Spectral Theory · Mathematics 2017-06-01 Rasoul Shafipour , Ali Khodabakhsh , Gonzalo Mateos , Evdokia Nikolova

Graph-based recommendation systems are effective at modeling collaborative patterns but often suffer from two limitations: overreliance on low-pass filtering, which suppresses user-specific signals, and omission of sequential dynamics in…

Information Retrieval · Computer Science 2025-09-25 Ahmad Bin Rabiah , Julian McAuley

Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent…

Information Theory · Computer Science 2021-11-08 Nazar Emirov , Cheng Cheng , Junzheng Jiang , Qiyu Sun

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so…

Machine Learning · Computer Science 2023-11-13 Christian Koke , Daniel Cremers

We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the…

Machine Learning · Computer Science 2018-10-04 Thomas Bonald , Alexandre Hollocou , Marc Lelarge

Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domains, there exist intuitive definitions of signals and…

Numerical Analysis · Mathematics 2018-04-06 John C. Urschel , Wenfang Xu , Ludmil T. Zikatanov

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…

Optimization and Control · Mathematics 2022-03-04 Quoc Van Tran , Hyo-Sung Ahn

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing…

Machine Learning · Computer Science 2017-10-06 Jean-Charles Vialatte , Vincent Gripon , Gilles Coppin