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Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…

Signal Processing · Electrical Eng. & Systems 2025-10-14 Mingzhi Wang , Zhichao Zhang

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…

Functional Analysis · Mathematics 2013-07-23 David I Shuman , Benjamin Ricaud , Pierre Vandergheynst

We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for…

Machine Learning · Computer Science 2022-11-28 Hongyu Guo , Yongyi Mao

Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal…

Signal Processing · Electrical Eng. & Systems 2019-12-30 Ljubisa Stankovic , Danilo P. Mandic , Milos Dakovic , Bruno Scalzo , Milos Brajovic , Ervin Sejdic , Anthony G. Constantinides

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

Numerical Analysis · Mathematics 2025-07-11 Robert Carlson

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…

Discrete Mathematics · Computer Science 2015-06-12 David I Shuman , Sunil K. Narang , Pascal Frossard , Antonio Ortega , Pierre Vandergheynst

A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…

Signal Processing · Electrical Eng. & Systems 2019-09-18 Bruno Scalzo Dees , Ljubisa Stankovic , Milos Dakovic , Anthony G. Constantinides , Danilo P. Mandic

Given a function $f$ in a finite field ${\mathbb F}_q$ of $q$ elements, we define the functional graph of $f$ as a directed graph on $q$ nodes labelled by the elements of ${\mathbb F}_q$ where there is an edge from $u$ to $v$ if and only if…

Number Theory · Mathematics 2015-05-27 Sergei V. Konyagin , Florian Luca , Bernard Mans , Luke Mathieson , Min Sha , Igor E. Shparlinski

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

Numerical Analysis · Mathematics 2025-08-26 Oleg Davydov

We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function…

Combinatorics · Mathematics 2022-01-12 Takashi Komatsu , Norio Konno , Iwao Sato , Shunya Tamura

Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation…

Machine Learning · Computer Science 2020-03-05 Alejandro Parada-Mayorga , Luana Ruiz , Alejandro Ribeiro

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…

Signal Processing · Electrical Eng. & Systems 2024-09-09 Yanan Zhao , Xingchao Jian , Feng Ji , Wee Peng Tay , Antonio Ortega

Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a…

Signal Processing · Electrical Eng. & Systems 2023-03-30 Feng Ji , Wee Peng Tay , Antonio Ortega

Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains.…

Machine Learning · Computer Science 2024-06-03 Haitao Mao , Zhikai Chen , Wenzhuo Tang , Jianan Zhao , Yao Ma , Tong Zhao , Neil Shah , Mikhail Galkin , Jiliang Tang

Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its…

Machine Learning · Computer Science 2020-08-26 Padraig Corcoran

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we…

General Mathematics · Mathematics 2022-10-11 Fang-Jia Yan , Bing-Zhao Li

Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the…

Information Retrieval · Computer Science 2025-02-26 Zenghui Chang , Yiqiao Zhang , Hong Cai Chen

Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…

Signal Processing · Electrical Eng. & Systems 2023-03-13 Feng Ji , Wee Peng Tay

BCI Motor Imagery datasets usually are small and have different electrodes setups. When training a Deep Neural Network, one may want to capitalize on all these datasets to increase the amount of data available and hence obtain good…

Signal Processing · Electrical Eng. & Systems 2022-11-07 Yassine El Ouahidi , Lucas Drumetz , Giulia Lioi , Nicolas Farrugia , Bastien Pasdeloup , Vincent Gripon

Graph signal processing (GSP) leverages the inherent signal structure within graphs to extract high-dimensional data without relying on translation invariance. It has emerged as a crucial tool across multiple fields, including learning and…

General Mathematics · Mathematics 2025-02-21 Yu Zhang , Bing-Zhao Li