Related papers: Graphon Signal Processing
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…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…
Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from 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…
In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple GFT designs that can capture different types of variation over the digraph…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
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…
In this work, we explore the interplay between graph limit theory, the geometry of underlying probability spaces, spectral theory, and network dynamical systems. We investigate two primary questions concerning forward and inverse…
A recent paper, ``A Graphon-Signal Analysis of Graph Neural Networks'', by Levie, analyzed message passing graph neural networks (MPNNs) by embedding the input space of MPNNs, i.e., attributed graphs (graph-signals), to a space of…
The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal…
Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph…
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…
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…
Fokker-Planck equations represent a suitable description of the finite-time behavior for a large class of particle systems as the size of the population tends to infinity. Recently, the theory of graph limits has been introduced in the…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, i.e., those determined by finitely many subgraph densities, are of particular interest because of their relation to various…