Related papers: Graph Fourier Transform: A Stable Approximation
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 Transformers (GTs) have demonstrated superior performance compared to traditional message-passing graph neural networks in many studies, especially in processing graph data with long-range dependencies. However, GTs tend to suffer…
Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. Recent research has focused on developing GSP-based methods for state estimation, attack detection, and…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
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…
Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered…
Transformers have achieved remarkable success in time series modeling, yet their internal mechanisms remain opaque. This work demystifies the Transformer encoder by establishing its fundamental equivalence to a Graph Convolutional Network…
Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
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…
Recently, an approach to graph signal processing based on graphons was proposed. Here we show how such a graphon-driven approach to the Fourier transform can be used on graphs sampled from a stochastic block model (SBM). In particular, we…
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…
The effective representation, precessing, analysis, and visualization of large-scale structured data over graphs are gaining a lot of attention. So far most of the literature has focused on real-valued signals. However, signals are often…
Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to…
Graph neural networks (GNNs) have achieved remarkable success in a variety of machine learning tasks over graph data. Existing GNNs usually rely on message passing, i.e., computing node representations by gathering information from the…
Motivation: A pan-genome graph represents a collection of genomes and encodes sequence variations between them. It is a powerful data structure for studying multiple similar genomes. Sequence-to-graph alignment is an essential step for the…
The analysis of the brain surface modeled as a graph mesh is a challenging task. Conventional deep learning approaches often rely on data lying in the Euclidean space. As an extension to irregular graphs, convolution operations are defined…
Time-frequency (T-F) domain methods for monaural speech enhancement have benefited from the success of deep learning. Recently, focus has been put on designing two-stream network models to predict amplitude mask and phase separately, or,…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A…