Related papers: Spectral graph fractional Fourier transform for di…
Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph…
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.…
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…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
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…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
In Graph Signal Processing (GSP), data dependencies are represented by a graph whose nodes label the data and the edges capture dependencies among nodes. The graph is represented by a weighted adjacency matrix $A$ that, in GSP, generalizes…
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website,…
This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an…
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…
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…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
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…
Graph filtering is a fundamental tool in graph signal processing. Polynomial graph filters (PGFs), defined as polynomials of a fundamental graph operator, can be implemented in the vertex domain, and usually have a lower complexity than…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
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…