Related papers: Graph Fourier transform based on singular value de…
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…
On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…
In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled…
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…
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…
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…
Graph Transformers (GTs) have demonstrated remarkable performance in graph representation learning over popular graph neural networks (GNNs). However, self--attention, the core module of GTs, preserves only low-frequency signals in graph…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and…
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…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role…
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…
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…
Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in spectral…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and…
Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian…