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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

How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…

Statistics Theory · Mathematics 2015-12-11 Subhadeep Mukhopadhyay

The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a…

funct-an · Mathematics 2008-02-03 Jayakumar Ramanathan , Pankaj Topiwala

Graph learning has a wide range of applications in many scenarios, which require more need for data privacy. Federated learning is an emerging distributed machine learning approach that leverages data from individual devices or data centers…

Machine Learning · Computer Science 2023-07-20 Peilin Liu , Yanni Tang , Mingyue Zhang , Wu Chen

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…

Signal Processing · Electrical Eng. & Systems 2018-03-28 Antonio Ortega , Pascal Frossard , Jelena Kovačević , José M. F. Moura , Pierre Vandergheynst

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian…

Functional Analysis · Mathematics 2017-03-20 Matthew Begué , Kasso A. Okoudjou

Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…

Signal Processing · Electrical Eng. & Systems 2022-12-21 T. Mitchell Roddenberry , Fernando Gama , Richard G. Baraniuk , Santiago Segarra

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

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Machine Learning · Computer Science 2024-06-05 Hongkang Li , Meng Wang , Tengfei Ma , Sijia Liu , Zaixi Zhang , Pin-Yu Chen

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…

Neural and Evolutionary Computing · Computer Science 2026-03-31 Hendrik Richter , Frank Neumann

Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper…

Information Theory · Computer Science 2017-08-23 Santiago Segarra , Gonzalo Mateos , Antonio G. Marques , Alejandro Ribeiro

In this paper, we develop a signal processing framework of a network without explicit knowledge of the network topology. Instead, we make use of knowledge on the distribution of operators on the network. This makes the framework flexible…

Signal Processing · Electrical Eng. & Systems 2020-12-14 Feng Ji , Wee Peng Tay

Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…

Combinatorics · Mathematics 2021-12-01 Raffaella Mulas

We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of…

Data Structures and Algorithms · Computer Science 2018-04-02 Andrew V. Knyazev

Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…

Signal Processing · Electrical Eng. & Systems 2020-11-24 Siavash Mollaebrahim , Baltasar Beferull-Lozano

In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…

Signal Processing · Electrical Eng. & Systems 2024-01-17 Semin Kwak , Laura Shimabukuro , Antonio Ortega

The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…

Signal Processing · Electrical Eng. & Systems 2019-10-02 Keng-Shih Lu , Antonio Ortega

We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or $\delta$-type), which show how various types of changes of a local or…

Spectral Theory · Mathematics 2019-10-21 Gregory Berkolaiko , James B. Kennedy , Pavel Kurasov , Delio Mugnolo

We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a…

Signal Processing · Electrical Eng. & Systems 2025-01-29 Bastian Seifert , Chris Wendler , Markus Püschel

We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target…

Machine Learning · Statistics 2018-03-21 Arun Venkitaraman , Saikat Chatterjee , Peter Händel