Related papers: A noncommutative approach to the graphon Fourier t…
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…
Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
We consider the task of representing signals supported on graph bundles, which are generalizations of product graphs that allow for "twists" in the product structure. Leveraging the localized product structure of a graph bundle, we…
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…
We consider the problem of estimating graph limits, known as graphons, from observations of sequences of sparse finite graphs. In this paper we show a simple method that can shed light on a subset of sparse graphs. The method involves…
To analyze data supported by arbitrary graphs G, DSP has been extended to Graph Signal Processing (GSP) by redefining traditional DSP concepts like shift, filtering, and Fourier transform among others. This paper revisits modulation,…
In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…
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…
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…
Graphons are analytic objects representing convergent sequences of large graphs. A graphon is said to be finitely forcible if it is determined by finitely many subgraph densities, i.e., if the asymptotic structure of graphs represented by…
We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections…
Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful feature representations from network data. However, on large-scale graphs convolutions incur in high computational cost, leading to…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
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 signal processing (GSP) leverages the inherent signal structure within graphs to extract high-dimensional data without relying on translation invariance. It has emerged as a crucial tool across multiple fields, including learning and…
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…
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
An important problem in the field of graph signal processing is developing appropriate overcomplete dictionaries for signals defined on different families of graphs. The Cayley graph of the symmetric group has natural applications in ranked…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…