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Related papers: Shift-invariant spaces on finite undirected graphs

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The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…

Dynamical Systems · Mathematics 2024-08-06 Christian Bick , Davide Sclosa

Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…

Machine Learning · Computer Science 2024-09-16 Samuel Rey , Madeline Navarro , Victor M. Tenorio , Santiago Segarra , Antonio G. Marques

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…

Signal Processing · Electrical Eng. & Systems 2018-03-01 Stephen Kruzick , José M. F. Moura

Graph Neural Networks (GNNs) have established themselves as the leading models for learning on graph-structured data, generally categorized into spatial and spectral approaches. Central to these architectures is the Graph Shift Operator…

Machine Learning · Computer Science 2026-02-09 Yassine Abbahaddou

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

Recently, a one-to-one correspondence between non-trivial non-Hermitian topology and directional amplification has been demonstrated, theoretically and experimentally, for the case of one complex band. Here, we extend our framework to…

Mesoscale and Nanoscale Physics · Physics 2025-09-25 Clara C. Wanjura , Andreas Nunnenkamp

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…

Functional Analysis · Mathematics 2009-12-22 David K Hammond , Pierre Vandergheynst , Rémi Gribonval

Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed…

Machine Learning · Computer Science 2025-02-28 Chaohao Yuan , Kangfei Zhao , Ercan Engin Kuruoglu , Liang Wang , Tingyang Xu , Wenbing Huang , Deli Zhao , Hong Cheng , Yu Rong

We propose a graph neural network (GNN) architecture to optimize base station (BS) beamforming and reconfigurable intelligent surface (RIS) phase shifts in a multi-RIS assisted wireless network. We create a bipartite graph model to…

Signal Processing · Electrical Eng. & Systems 2025-01-28 Byungju Lim , Mai Vu

A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…

Quantum Physics · Physics 2025-11-18 Zhen-Peng Xu , Jie Wang , Qi Ye , Gereon Koßmann , René Schwonnek , Andreas Winter

We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…

Functional Analysis · Mathematics 2024-08-07 José Luis Romero , Alexander Ulanovskii , Ilya Zlotnikov

Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models…

Machine Learning · Statistics 2026-03-19 Nil Ayday , Lingchu Yang , Debarghya Ghoshdastidar

The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. These subgraphs counting invariants are not algebraically independent. In our view…

Combinatorics · Mathematics 2008-12-11 Tomi Mikkonen

We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown…

Computational Physics · Physics 2020-06-15 Surya Effendy , Juhyun Song , Martin Z. Bazant

Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the…

Systems and Control · Computer Science 2016-09-22 Elvin Isufi , Geert Leus , Paolo Banelli

Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine…

Machine Learning · Computer Science 2024-09-17 Jingwei Guo , Kaizhu Huang , Xinping Yi , Zixian Su , Rui Zhang

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

We consider the question whether, given a countable system of lattices $(\Gamma_j)_{j \in J}$ in a locally compact abelian group $G$, there exists a sequence of functions $(g_j)_{j \in J}$ such that the resulting generalized shift-invariant…

Functional Analysis · Mathematics 2017-06-01 Hartmut Führ , Jakob Lemvig

The Earth's surface is subject to complex and dynamic processes, ranging from large-scale phenomena such as tectonic plate movements to localized changes associated with ecosystems, agriculture, or human activity. Satellite images enable…

Computer Vision and Pattern Recognition · Computer Science 2026-03-02 Corentin Dufourg , Charlotte Pelletier , Stéphane May , Sébastien Lefèvre

Finite metric spaces are characterized by a polyhedral cone defined in terms of the positivity of the distance functions and the triangle inequalities. Their classification is based on the decomposition of an associated polyhedral cone,…

Combinatorics · Mathematics 2020-03-09 Ayse Humeyra Bilge , Metehan Incegul