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Related papers: Wavelets on Graphs via Spectral Graph Theory

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We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform.…

Machine Learning · Computer Science 2019-04-17 Bingbing Xu , Huawei Shen , Qi Cao , Yunqi Qiu , Xueqi Cheng

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…

Discrete Mathematics · Computer Science 2017-10-24 Madeleine S. Kotzagiannidis , Pier Luigi Dragotti

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

Machine Learning · Computer Science 2020-10-29 Yin-Cong Zhi , Yin Cheng Ng , Xiaowen Dong

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

We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the…

Functional Analysis · Mathematics 2015-03-19 Raif M. Rustamov

In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…

Computer Vision and Pattern Recognition · Computer Science 2015-05-20 Idan Ram , Michael Elad , Israel Cohen

Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although…

Machine Learning · Computer Science 2023-05-04 Lequan Lin , Junbin Gao

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…

Functional Analysis · Mathematics 2021-11-02 Harry Sevi , Gabriel Rilling , Pierre Borgnat

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

Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on…

Machine Learning · Computer Science 2025-08-12 Shay Deutsch , Lionel Yelibi , Alex Tong Lin , Arjun Ravi Kannan

Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To…

Numerical Analysis · Mathematics 2015-09-24 Ana Susnjara , Nathanael Perraudin , Daniel Kressner , Pierre Vandergheynst

Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…

Signal Processing · Electrical Eng. & Systems 2017-11-07 Nicolas Tremblay , Paulo Gonçalves , Pierre Borgnat

In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or…

Signal Processing · Electrical Eng. & Systems 2025-04-10 Chun Hei Michael Chan , Alexandre Cionca , Dimitri Van De Ville

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…

Machine Learning · Computer Science 2026-02-18 Valentin de Bassompierre , Jean-Charles Delvenne , Laurent Jacques

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal…

Information Theory · Computer Science 2013-12-10 J. D. McEwen , P. Vandergheynst , Y. Wiaux

We propose a combination of a variational autoencoder and a transformer based model which fully utilises graph convolutional and graph pooling layers to operate directly on graphs. The transformer model implements a novel node encoding…

Machine Learning · Computer Science 2021-04-12 Joshua Mitton , Hans M. Senn , Klaas Wynne , Roderick Murray-Smith

Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…

Information Retrieval · Computer Science 2023-12-07 Osama Alshareet , A. Ben Hamza

Signal analysis on graphs relies heavily on the graph Fourier transform, which is defined as the projection of a signal onto an eigenbasis of the associated shift operator. Large graphs of similar structure may be represented by a graphon.…

Combinatorics · Mathematics 2024-06-26 Mahya Ghandehari , Jeannette Janssen , Nauzer Kalyaniwalla

We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…

Information Theory · Computer Science 2013-08-15 B. Leistedt , J. D. McEwen

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…

Signal Processing · Electrical Eng. & Systems 2023-06-28 Ka Man Yim , Jacob Leygonie