Related papers: Hilbert Transform on Graphs: Let There Be Phase
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
Learning representations on large graphs is a long-standing challenge due to the inter-dependence nature. Transformers recently have shown promising performance on small graphs thanks to its global attention for capturing all-pair…
Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix…
Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
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…
In recent years, improvements in various image acquisition techniques gave rise to the need for adaptive processing methods, aimed particularly for large datasets corrupted by noise and deformations. In this work, we consider datasets of…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
Graph Transformers (GTs) have demonstrated remarkable performance in graph representation learning over popular graph neural networks (GNNs). However, self--attention, the core module of GTs, preserves only low-frequency signals in graph…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can…