Related papers: A Hilbert Space Theory of Generalized Graph Signal…
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…
We formulate and prove the existence and uniqueness of the generalized Fourier transform associated with the absolutely continuous part of an arbitrary selfadjoint operator on a separable Hilbert space. To this end we develop a novel method…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives -- were…
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…
In Graph Signal Processing (GSP), data dependencies are represented by a graph whose nodes label the data and the edges capture dependencies among nodes. The graph is represented by a weighted adjacency matrix $A$ that, in GSP, generalizes…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several…
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
Graph learning, or network inference, is a prominent problem in graph signal processing (GSP). GSP generalizes the Fourier transform to non-Euclidean domains, and graph learning is pivotal to applying GSP when these domains are unknown.…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
In network science, the interplay between dynamical processes and the underlying topologies of complex systems has led to a diverse family of models with different interpretations. In graph signal processing, this is manifested in the form…
Graph neural networks (GNN) have shown outstanding applications in many fields where data is fundamentally represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many…
Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models…
Predicting the labels of graph-structured data is crucial in scientific applications and is often achieved using graph neural networks (GNNs). However, when data is scarce, GNNs suffer from overfitting, leading to poor performance.…
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…
Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…
Graph Neural Networks (GNNs) have demonstrated effectiveness in collaborative filtering tasks due to their ability to extract powerful structural features. However, combining the graph features extracted from user-item interactions and…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…