Related papers: Stratified Graph Spectra
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…
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 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.…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
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…
Classical Graph Signal Processing (GSP) provides a robust framework for analyzing signals on irregular domains, utilizing the graph Fourier transform as a cornerstone for spectral analysis and filtering. However, as data structures grow in…
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.…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
The paper presents the graph Fourier transform (GFT) of a signal in terms of its spectral decomposition over the Jordan subspaces of the graph adjacency matrix $A$. This representation is unique and coordinate free, and it leads to…
The definition of the graph Fourier transform is a fundamental issue in graph signal processing. Conventional graph Fourier transform is defined through the eigenvectors of the graph Laplacian matrix, which minimize the $\ell_2$ norm signal…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
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…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
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…
Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…
Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation…
In this paper, we explore the topic of graph learning from the perspective of the Irregularity-Aware Graph Fourier Transform, with the goal of learning the graph signal space inner product to better model data. We propose a novel method to…
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…