Related papers: What's in a frequency: new tools for graph Fourier…
The design of Graph Transformers (GTs) generally neglects considerations for fairness, resulting in biased outcomes against certain sensitive subgroups. Since GTs encode graph information without relying on message-passing mechanisms,…
A new scheme to sample signals defined in the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…
Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to…
Optical spectrum analysis is the cornerstone of spectroscopic sensing, optical network performance monitoring, and hyperspectral imaging. While conventional high-performance spectrometers used to perform such analysis are often large…
We propose Hilbert transform (HT) and analytic signal (AS) construction for signals over graphs. This is motivated by the popularity of HT, AS, and modulation analysis in conventional signal processing, and the observation that…
Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation…
How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…
Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…
With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph…
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…
The analysis of multi-dimensional graph signals on complex structured domains remains a fundamental challenge,
We study estimation of piecewise smooth signals over a graph. We propose a $\ell_{2,0}$-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
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…
The recent works proposing transformer-based models for graphs have proven the inadequacy of Vanilla Transformer for graph representation learning. To understand this inadequacy, there is a need to investigate if spectral analysis of the…
We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform.…
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…