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Related papers: Shift-invariant spaces on finite undirected graphs

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The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…

Functional Analysis · Mathematics 2019-12-06 Alexandru Aleman , Rui Pacheco , John C. Wood

Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on…

Machine Learning · Computer Science 2018-11-13 Jiatao Jiang , Zhen Cui , Chunyan Xu , Jian Yang

Feature-based image matching has extensive applications in computer vision. Keypoints detected in images can be naturally represented as graph structures, and Graph Neural Networks (GNNs) have been shown to outperform traditional deep…

Computer Vision and Pattern Recognition · Computer Science 2025-08-29 Xianfeng Song , Yi Zou , Zheng Shi , Zheng Liu

We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral…

Machine Learning · Computer Science 2020-06-11 Edouard Oyallon

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…

Computer Vision and Pattern Recognition · Computer Science 2017-03-02 Renata Khasanova , Pascal Frossard

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…

Signal Processing · Electrical Eng. & Systems 2025-09-23 Daxiang Li , Zhichao Zhang

Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…

Image and Video Processing · Electrical Eng. & Systems 2024-11-26 Alessandro Gnutti , Fabrizio Guerrini , Riccardo Leonardi , Antonio Ortega

The graph Laplacian is an important tool in Graph Signal Processing (GSP) as its eigenvalue decomposition acts as an analogue to the Fourier transform and is known as the Graph Fourier Transform (GFT). The line graph has a GFT that is a…

Signal Processing · Electrical Eng. & Systems 2019-10-23 Ian M. T. Rooney , Parker S. Kuklinski , David A. Hague

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…

Signal Processing · Electrical Eng. & Systems 2020-01-08 Feng Ji , Wee Peng Tay

Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…

Machine Learning · Statistics 2025-11-21 Feiyue Zhao , Yangfan He , Zhichao Zhang

Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…

Machine Learning · Computer Science 2021-04-27 Giuseppe Patanè

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

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle…

Machine Learning · Computer Science 2024-03-11 Zeyang Zhang , Xin Wang , Ziwei Zhang , Zhou Qin , Weigao Wen , Hui Xue , Haoyang Li , Wenwu Zhu

Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under…

Machine Learning · Computer Science 2026-03-16 Tianyin Liao , Ziwei Zhang , Yufei Sun , Chunyu Hu , Jianxin Li

We discuss some structural properties of finitely generated shift-invariant (FGSI) spaces and subspaces of Sobolev spaces, particularly those related to convolution and the product within these spaces. We find shift-invariant solutions in…

Functional Analysis · Mathematics 2025-05-02 Aleksandar Aksentijević , Suzana Aleksić , Stevan Pilipović

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…

Information Theory · Computer Science 2017-05-26 Geert Leus , Santiago Segarra , Alejandro Ribeiro , Antonio G. Marques

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…

Machine Learning · Computer Science 2021-03-11 Masanobu Horie , Naoki Morita , Toshiaki Hishinuma , Yu Ihara , Naoto Mitsume

Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…

Signal Processing · Electrical Eng. & Systems 2026-03-03 Mingzhi Wang , Manjun Cui , Feiyue Zhao , Yangfan He , Zhichao Zhang

Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…

Signal Processing · Electrical Eng. & Systems 2019-03-22 Benjamin Girault , Antonio Ortega

Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…

Machine Learning · Computer Science 2022-02-01 Ying-Xin Wu , Xiang Wang , An Zhang , Xiangnan He , Tat-Seng Chua