Related papers: Fourier transform of vector-valued graph signals
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…
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…
Our principal result is the following. Let $X$ and $Y$ be Banach spaces, let $G$ be a locally compact abelian group, and let $K$ be an operator valued kernel defined on $G$ with values in the space of bounded linear operators from $X$ to…
Graph transformation that predicts graph transition from one mode to another is an important and common problem. Despite much progress in developing advanced graph transformation techniques in recent years, the fundamental assumption…
This paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets.…
This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the…
In this paper, we introduce translation operators on graphs. Contrary to spectrally-defined translations in the framework of graph signal processing, our operators mimic neighborhood-preserving properties of translation operators defined in…
The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the…
Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can…
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data.…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. While recent advances have enabled graph topology learning from observed signals, existing…
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.
Recently, Transformer model, which has achieved great success in many artificial intelligence fields, has demonstrated its great potential in modeling graph-structured data. Till now, a great variety of Transformers has been proposed to…
Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable…
Incorporating graphs in the analysis of multivariate signals is becoming a standard way to understand the interdependency of activity recorded at different sites. The new research frontier in this direction includes the important problem of…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks).…
Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…