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Distributed graph filters have found applications in wireless sensor networks (WSNs) to solve distributed tasks such as consensus, signal denoising, and reconstruction. However, when employed over WSN, the graph filters should deal with the…

In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…

This paper proposes a class of $M$-channel spectral graph filter banks with a symmetric structure, that is, the transform has sampling operations and spectral graph filters on both the analysis and synthesis sides. The filter banks achieve…

An Abstract Graph Machine(AGM) is an abstract model for distributed memory parallel stabilizing graph algorithms. A stabilizing algorithm starts from a particular initial state and goes through series of different state changes until it…

This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and…

We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a…

A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…

This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…

This paper focuses on devising graph signal processing tools for the treatment of data defined on the edges of a graph. We first show that conventional tools from graph signal processing may not be suitable for the analysis of such signals.…

Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or gets extinct. The outcome naturally depends on the…

Ordering the collection of states of a given automaton starting from an order of the underlying alphabet is a natural move towards a computational treatment of the language accepted by the automaton. Along this path, Wheeler \emph{graphs}…

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…

Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…

Ranked data sets, where m judges/voters specify a preference ranking of n objects/candidates, are increasingly prevalent in contexts such as political elections, computer vision, recommender systems, and bioinformatics. The vote counts for…

Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…