Related papers: Translation Operator in Graph Signal Processing: A…
Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…
Generalized from image and language translation, graph translation aims to generate a graph in the target domain by conditioning an input graph in the source domain. This promising topic has attracted fast-increasing attention recently.…
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…
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…
A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for…
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…
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…
Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…
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…
Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models…
As graph representations of data emerge in multiple domains, data analysts need to be able to intelligently select among a magnitude of different data graphs based on the effects different graph operators have on them. Exhaustive execution…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…
In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.
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…