Related papers: On the Shift Operator, Graph Frequency and Optimal…
We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each…
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.…
Graph signal processing (GSP) studies graph-structured data, where the central concept is the vector space of graph signals. To study a vector space, we have many useful tools up our sleeves. However, uncertainty is omnipresent in practice,…
We propose a framework for generalized sampling of graph signals that parallels sampling in shift-invariant (SI) subspaces. This framework allows for arbitrary input signals, which are not constrained to be bandlimited. Furthermore, the…
Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network…
To address the peculiarities of directed and/or signed graphs, new Laplacian operators have emerged. For instance, in the case of directionality, we encounter the magnetic operator, dilation (which is underexplored), operators based on…
In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise…
Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for…
Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under…
This paper addresses the problem of selecting an optimal sampling set for signals on graphs. The proposed sampling set selection (SSS) is based on a localization operator that can consider both vertex domain and spectral domain…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
Signal processing over single-layer graphs has become a mainstream tool owing to its power in revealing obscure underlying structures within data signals. However, many real-life datasets and systems, {including those in Internet of Things…
Graph filter design is central to spectral collaborative filtering, yet most existing methods rely on manually tuned hyperparameters rather than fully learnable filters. We show that this challenge stems from a bias in traditional…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…
The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands…
A graph operator is a function $\Gamma$ defined on some set of graphs such that whenever two graphs $G$ and $H$ are isomorphic, written $G\simeq H$, then $\Gamma(G)\simeq \Gamma(H)$. For a graph $G$ not in the domain of $\Gamma$, we put…
Transformers, renowned for their self-attention mechanism, have achieved state-of-the-art performance across various tasks in natural language processing, computer vision, time-series modeling, etc. However, one of the challenges with deep…
Reservoir computing has been successfully applied to graphs as a preprocessing method to improve the training efficiency of Graph Neural Networks (GNNs). However, a common issue that arises when repeatedly applying layer operators on graphs…
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired.…