Related papers: Graphon Signal Processing
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…
Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the…
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn…
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…
Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
Data processing tasks over graphs couple the data residing over the nodes with the topology through graph signal processing tools. Graph filters are one such prominent tool, having been used in applications such as denoising, interpolation,…
Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus,…
Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of…
Spectral graph neural networks learn graph filters, but their behavior with increasing depth and polynomial order is not well understood. We analyze these models in the graph Fourier domain, where each layer becomes an element-wise…
Graph convolution networks, like message passing graph convolution networks (MPGCNs), have been a powerful tool in representation learning of networked data. However, when data is heterogeneous, most architectures are limited as they employ…
The shift operation plays a crucial role in the classical signal processing. It is the generator of all the filters and the basic operation for time-frequency analysis, such as windowed Fourier transform and wavelet transform. With the…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…