Related papers: On Local Distributions in Graph Signal Processing

Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…

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…

In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed…

Graph neural networks (GNN) typically rely on localized message passing, requiring increasing depth to capture long range dependencies. In this work, we introduce Graph Linear Transformations, a linear transformation that realizes direct…

Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…

Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of…

Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus,…

Graph Neural Networks (GNNs) have emerged as highly successful tools for graph-related tasks. However, real-world problems involve very large graphs, and the compute resources needed to fit GNNs to those problems grow rapidly. Moreover, the…

We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message…

As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…

Over the past two decades, tools from network science have been leveraged to characterize the organization of both structural and functional networks of the brain. One such measure of network organization is hub node identification. Hubs…

Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…

This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such…

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…

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…