Related papers: Graphon Signal Processing
Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent…
Graph Neural Networks (GNNs) rely on graph convolutions to exploit meaningful patterns in networked data. Based on matrix multiplications, convolutions incur in high computational costs leading to scalability limitations in practice. To…
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…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…
In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…
Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the…
We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the…
We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
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…
Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or…
Recent advent in graph signal processing (GSP) has led to the development of new graph-based transforms and wavelets for image / video coding, where the underlying graph describes inter-pixel correlations. In this paper, we develop a new…
Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet of Things (IoT) paradigm. The recent emerging Graph Signal Processing field can also contribute to enabling the IoT by providing key tools, such as…
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.…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of…
Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since…
Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…