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Contrastive learning has emerged as a premier method for learning representations with or without supervision. Recent studies have shown its utility in graph representation learning for pre-training. Despite successes, the understanding of…

Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints,…

Graph signal processing represents an important advancement in the field of data analysis, extending conventional signal processing methodologies to complex networks and thereby facilitating the exploration of informative patterns and…

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard…

Financial spillovers in interconnected systems, such as global banking networks, require tools that capture temporal and frequency dynamics, while incorporating the underlying network topology. While current network time series models are…

A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…

We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…

Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space…

Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert…

In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…

Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…

Spectral computed tomography based on a photon-counting detector (PCD) attracts more and more attentions since it has the capability to provide more accurate identification and quantitative analysis for biomedical materials. The limited…

Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the…

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to…

Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…

In this paper, we consider Wiener filters to reconstruct deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement Wiener filters and…

Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather. In this paper, we propose a Graph Convolutional Recurrent Neural Network (GCRNN) architecture specifically…