Related papers: Node-Adaptive Regularization for Graph Signal Reco…

Graph representation learning, aiming to learn low-dimensional representations which capture the geometric dependencies between nodes in the original graph, has gained increasing popularity in a variety of graph analysis tasks, including…

In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…

Graph Neural Networks are notorious for its memory consumption. A recent Transformer-based GNN called Graph Transformer is shown to obtain superior performances when long range dependencies exist. However, combining graph data and…

Node classification on graphs is a significant task with a wide range of applications, including social analysis and anomaly detection. Even though graph neural networks (GNNs) have produced promising results on this task, current…

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…

A noise-corrupted image often requires interpolation. Given a linear denoiser and a linear interpolator, when should the operations be independently executed in separate steps, and when should they be combined and jointly optimized? We…

This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms…

Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been…

With the rapid growth of graph-structured data in critical domains, unsupervised graph-level anomaly detection (UGAD) has become a pivotal task. UGAD seeks to identify entire graphs that deviate from normal behavioral patterns. However,…

In this paper we show that simple noise regularisation can be an effective way to address GNN oversmoothing. First we argue that regularisers addressing oversmoothing should both penalise node latent similarity and encourage meaningful node…

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure,…

In this paper, we propose a novel graph-based approach for semi-supervised learning problems, which considers an adaptive adjacency of the examples throughout the unsupervised portion of the training. Adjacency of the examples is inferred…

The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…

Graph Neural Networks (GNNs) have gained significant popularity for learning representations of graph-structured data due to their expressive power and scalability. However, despite their success in domains such as social network analysis,…

It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…

In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks,…

While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…